Scientific Journals and Yearbooks Published at SAS
Article List
Tatra Mountains Mathematical Publications
Volume 34, 2006, No. 2
Content:
- Sarsak, M. - Ganster, M. - Steiner, M.
On $Si$-metacompact spaces.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 1-7. - Kupka, I.
Metafunctions.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 9-18. - Drozdowski, R.
On the structure of some subsets in the space of functions of bounded $Λ$-variation.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 19-27. - Filipczak, M. - Terepeta, M.
On continuity concerned with $ψ$-density topologies.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 29-36. - Filipczak, M. - Filipczak, T.
A generalization of the density topology.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 37-47. - Nowik, A.
On combinatorial properties of Borel generated $σ$-ideals related to the property $(
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 49-60. - Domnik, I.
On quasi-oscillation for symmetrical quasi-continuity.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 61-69. - Matejdes, M.
Minimal multifunctions and the cluster sets.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 71-76. - Jankech, A.
The construction and some properties of cluster multifunction.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 77-82. - Loranty, A.
The $langle s angle$-density topology is not generated.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 83-91. - Mikucka, A.
On graph quasi-continuous functions.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 93-105. - Pasteka, M.
The measurability of the product of arithmetic progressions.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 107-111. - Czarnowska, J.
Connectivity property of multivalued maps.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 113-117. - Haluska, J. - Hutnik, O.
On algebras of symmetrical associative aggregation operators related to means.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 119-133. - Hejduk, J.
On the cardinality size of the homeomorphic density type topologies.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 135-139. - Filipczak, M. - Filipczak, T.
Remarks on $f$-density and $ψ$-density.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 141-149. - Horbaczewska, G.
On $I$-density topologies with respect to a fixed sequence—further properties.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 151-157. - Holy, D. - Matejicka, L.
C-upper semicontinuous and C$*$-upper semicontinuous multifunctions.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 159-165. - Strońska, E.
On the extension of some functions to $Qs1$-functions and on the sums of two $Qs1$-functions.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 167-172. - Grande, Z.
When the derivatives of solutions of the Cauchy's problem are $(S)$-continuous?.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 173-177. - Grande, Z.
On the convergence of sequences of $(A, B)$-quasicontinuous functions.
In Tatra Mountains Mathematical Publications. Vol. 34, no. 2 (2006), p. 179-181.
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On $Si$-metacompact spaces Mohammad S. Sarsak 1), Maximilian Ganster 2), Markus Steiner 3)
The primary purpose of this paper is to introduce and study new variations of metacompactness by utilizing semi-open sets. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 1-7. | ||||||||
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Metafunctions Ivan Kupka 1)
In this article a new notion is introduced. This notion (metafunction) is a generalization of the notion of multifunction. Some examples of metafunctions are shown. Various continuity properties of metafunctions are defined and investigated. It is shown that a metafunction, which represents some kind of ``inverse mapping'' to the Lebesque measure, has strong continuity properties. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 9-18. | ||||||||
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On the structure of some subsets in the space of functions of bounded $Λ$-variation Robert Drozdowski 1)
In the paper [D. Waterman: On $Łambda$-bounded variation, Studia Math. 57 (1976), 33–45] a concept of functions of bounded $Łambda$-variation was introduced. In this paper the structure of different subsets of the space of $Łambda$-bounded variation is described. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 19-27. | ||||||||
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On continuity concerned with $ψ$-density topologies Małgorzata Filipczak 1), Małgorzata Terepeta 2)
This paper is concerned with three kinds of topologies: the natural topology, density topology and $ψ$-density topology on the real line. We can consider different classes of continuous functions using these topologies on the domain and the range of functions. They can be compared with the classes of Baire 1, Baire*1 and Darboux functions. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 29-36. | ||||||||
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A generalization of the density topology Małgorzata Filipczak 1), Tomasz Filipczak 2)
In the paper we introduce a notion of $f$-density point of the measurable set on the real line. This notion is a generalization of Lebesgue density and also of $ψ$-density which was introduced in [S. J. Taylor: On strengthening the Lebesgue density theorem, Fund. Math. 46 (1959) 395–315]. We examine basic properties of an $f$-density and of a topology generated by it. Moreover, we investigate relationships between $f$-density and Lebesgue density and between $f$-densities for different functions $f$. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 37-47. | ||||||||
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On combinatorial properties of Borel generated $σ$-ideals related to the property $( Andrzej Nowik 1)
We consider a strengthening of $(P)$ property and other notions of $σ$-ideals. In particular, we prove that every transitive weakly $Gδ$ generated łinebreak $σ$-ideal has the strongest possible property in the hierarchy of properties related to $(operatorname P)$ property. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 49-60. | ||||||||
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On quasi-oscillation for symmetrical quasi-continuity Irena Domnik 1)
A classical oscillation (quasi-oscillation) characterizes the set of all points at which a function with values in a metric space is continuous (quasi-continuous). These conditions were introduced in [J. Borsik: Oscillation for quasicontinuity, Tatra Mt. Math. Publ. 14, (1998), 117–125], [J. Borsik: On quasioscillation, Tatra Mt. Math. Publ. 2, (1993), 25–36], [J. Ewert: Superpositions of oscillations and quasi-oscillations, Acta Math. Hungar. {bf 101}, (2003), 13–19], [P. Kostyrko: Some properties of oscillation, Math. Slovaca, 30, (1980), 157–162]. For the functions of two variables the symmetrical quasi-continuity (with respect to $x$ and $y$) can be considered. In this paper we define a quasi-oscillation for symmetrically quasi-continuous functions. We will give properties of this oscillation and a characterization of the symmetrical quasi-continuity with respect to $x$ (to $y$). Furthermore, we will study the convergence of a net of quasi-oscillations. Moreover, relationships between sets of points of continuity, symmetrical quasi-continuity, and quasi-continuity of the function are considered. For real function of two variables the Baire type (with respect to $x$ and $y$) functions are introduced. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 61-69. | ||||||||
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Minimal multifunctions and the cluster sets Milan Matejdes 1)
The paper deals with the minimal multifunctions which can be considered as the ``best'' selections closely related to continuous as well as quasi-continuous selections. We will give a characterization of minimal multifunction with closed graph by a cluster multifunction with respect to open sets. The conditions under which minimal multifunction is single valued except for a set of first category are given. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 71-76. | ||||||||
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The construction and some properties of cluster multifunction Andrej Jankech 1)
We present the construction and some properties of cluster multifunction $CF$ concerning various types of generalized continuities depending on the properties of multifunction $F$ and the relation between sets $F(x)$ and $CF(x)$ at point $x$. Next we introduce some theorems concerning a set of all semi-continuity points of $CF$. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 77-82. | ||||||||
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The $langle s
angle$-density topology is not generated Anna Loranty 1)
There are presented some properties of real functions $f:Bbb{R} ightarrow Bbb{R}$ which are continuous when $łangle s angle$-density topology (for a sequence $łangle s angle$ such that $łiminfłimitsn ightarrow ∞((sn) / (sn+1))=0$) is used on both the domain and the range. For example, it is shown that such functions are $Baire*1$ functions. The main result concerns the property that the $łangle s angle$-density topology is not generated. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 83-91. | ||||||||
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On graph quasi-continuous functions Aneta Mikucka 1)
In the paper [Z. Grande: Sur les fonctions $A$-continues, Demonstratio Math. 11 (1978), 519–526] a concept of graph continuous functions was introduced. An idea of graph quasi-continuous functions and their properties was investigated in [A. Mikucka: Graph quasi-continuity, Demonstratio Math. 36 (2003), 483–494]. In this paper different properties of these functions are studied. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 93-105. | ||||||||
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The measurability of the product of arithmetic progressions Milan Pasteka 1)
This paper deals with arithmetic progressions and measurability in the sense of Buck. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 107-111. | ||||||||
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Connectivity property of multivalued maps Joanna Czarnowska 1)
The main purpose of the paper is to extend Fast theorem for a real function onto the multivalued maps case. proclaim{Theorem} ({ Fast}) Let $f:Bbb R×Bbb R oBbb R$ be a real function. There exists a function $u:I o Bbb R$ such that for any $yin Bbb R$ the function $fy+u$ has Darboux property. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 113-117. | ||||||||
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On algebras of symmetrical associative aggregation operators related to means Jan Haluska 1), Ondrej Hutnik 2)
The aim of this paper is to introduce and study algebras of symmetrical associative aggregation operators related to means (arithmetic, geometric, logarithmic, harmonic, etc.). Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 119-133. | ||||||||
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On the cardinality size of the homeomorphic density type topologies Jacek Hejduk 1)
The paper deals with the density type topologies generated by a nondecreasing and unbounded sequence of positive reals. The cardinality of family of the homeomorphic topological spaces equipped with such density type topologies is discussed. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 135-139. | ||||||||
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Remarks on $f$-density and $ψ$-density Małgorzata Filipczak 1), Tomasz Filipczak 2)
In [M. Filipczak, T. Filipczak: A generalization of the density topology, to appear] a notion of $f$-density point of a Lebesgue measurable set on the real line was introduced. It is a generalization of a well-known notion of density point and simultaneously a notion of the $ψ$@-density point, introduced by [S. J. Taylor: On strengthening the Lebesgue density theorem, Fund. Math. XLVI, (1959), 305–315]. We examine properties of topologies generated by $f$-density operators, for functions satisfying $łiminfx ightarrow 0+$ {$((f(x)) / x)=0$}, and their similarities to $ψ$@-density topologies. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 141-149. | ||||||||
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On $I$-density topologies with respect to a fixed sequence—further properties Grażyna Horbaczewska 1)
Some properties of topologies introduced similarly as the $I$-density topology are investigated. We also consider approximately continuous functions for these topologies. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 151-157. | ||||||||
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C-upper semicontinuous and C$*$-upper semicontinuous multifunctions Dusan Holy 1), Ladislav Matejicka
We express $c$-upper semicontinuous and $c*$-upper semicontinuous multifunctions in terms of active boundary (Frac) of multifunctions. Characterizations of locally compact and locally countably compact space in terms of $c$-upper semicontinuous and $c*$-upper semicontinuous multifunctions having closed graphs are given. We give some results when $c$-upper semicontinuity ($c*$-upper semicontinuity) of multifunctions implies $c$-upper semicontinuity ($c*$-upper semicontinuity) of corresponding graph multifunctions. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 159-165. | ||||||||
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On the extension of some functions to $Qs1$-functions and on the sums of two $Qs1$-functions Ewa Strońska 1)
A function $f:Bbb Rm o Bbb R$ satisfies the condition $Qs1$ at a point ${oldkey x}in Bbb Rm$ if for each real $ε > 0$ and for each set $U i {oldkey x}$ belonging to the density topology there is an open set $V$ such that $emptyset eq U cap V subset f-1((f({oldkey x})-ε, f({oldkey x}) +ε)) cap C(f)$, where $C(f)$ denotes the set of all continuity points of $f$. For a nonempty set $Asubset Bbb Rm$ it is proved that the Lebesgue measure $łambda (cl(A)ig)=0$ if and only if for each $łambda$-almost everywhere continuous function $f:Bbb Rm o Bbb R$ there is a function $gin Qs1$ such that $f|A = g|A$. Moreover, it is proved that every function $f:Bbb Rm o Bbb R$ satisfying the condition $łambda (cl(D(f)))=0,$ where $D(f)=Bbb Rm setminus C(f)$, is the sum of two functions $g,h:Bbb Rm o Bbb R$ with the condition $Qs1$. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 167-172. | ||||||||
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When the derivatives of solutions of the Cauchy's problem are $(S)$-continuous? Zbigniew Grande 1)
Some conditions implying that the derivatives of solutions of the Cauchy's problem $y'(x)=f(x, y (x))$, with an initial condition $y(x0)=y0$, are $(S)$-continuous or $(S)$-path continuous are presented. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 173-177. | ||||||||
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On the convergence of sequences of $(A, B)$-quasicontinuous functions Zbigniew Grande 1)
A set-theoretical generalization of well-known theorem on the cliquishness of the limit of a pointwise convergent sequence of quasicontinuous functions from Baire topological space to a metric space is formulated and proved in this article. Fulltext Tatra Mountains Mathematical Publications. Volume 34, 2006, No. 2: 179-181. |
