Scientific Journals and Yearbooks Published at SAS
Article List
Tatra Mountains Mathematical Publications
Volume 28, 2004, No. 1
Content:
- Ewert, J. - Kowalczyk, S.
On pt-spaces.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 1-10. - Sochaczewska, A.
Proximities defined by open covers and convergence of nets of multivalued maps.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 11-19. - Wesołowska, J.
On set of convergence points of transfinite sequence of quasi-continuous functions.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 21-27. - Grande, Z.
On Darboux $Bbb Q$-differentiable functions and Darboux wright convex function.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 29-33. - Kucner, J.
The space of the strong Świątkowski functions.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 35-42. - Ponomarev, S.
A note on $σ$-discrete and massive spaces.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 43-56. - Grande, Z. - Fatz-Grupka, A.
On countably continuous functions.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 57-63. - Szkibiel, G.
Semi-quasicontinuity and PU–CHEN–PU theorem.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 65-70. - Recław, I.
On non-measurable unions of sections of a Borel set.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 71-73. - Szaz, A.
Rare and meager sets in relator spaces.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 75-95. - Machura, M.
Cardinal invariants ${frak p}$, ${frak t}$ and ${frak h}$ and real functions.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 97-108. - Chmielewska, K.
Strong supmeasurability of functions of two variables.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 109-116. - Flak, K. - Łazarow, E. - Maliszewski, A.
Sums of $Scr T<b>I$-quasi-continuous functions.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 117-124. - Papco, M.
On measurable spaces and measurable maps.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 125-140. - Kwiecińska, G.
Note on the sup-measurability of multivalued functions.
In Tatra Mountains Mathematical Publications. Vol. 28, no. 1 (2004), p. 141-151.
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On pt-spaces Janina Ewert 1), Stanisław Kowalczyk 2)
The research in the selection theory led to define some class of topological spaces, so called pt-spaces. In this paper the relations between pt-spaces and other classes of ones are studied. It is also shown that each Hausdorff pt-space is a Baire space and that any locally compact paracompact space is a pt-space. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 1-10. | ||||||||
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Proximities defined by open covers and convergence of nets of multivalued maps Agata Sochaczewska 1)
Proximities defined by open covers and convergence of nets of multivalued maps are investigated. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 11-19. | ||||||||
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On set of convergence points of transfinite sequence of quasi-continuous functions Jolanta Wesołowska 1)
The aim of the paper is to characterize the class of sets of points at which a transfinite sequence of quasi-continuous real functions converges. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 21-27. | ||||||||
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On Darboux $Bbb Q$-differentiable functions and Darboux wright convex function Zbigniew Grande 1)
It is shown that for each function $f:Bbb R o Bbb R$ there is an additive almost continuous function $g$ (an additive function $h$) such that the sum $f + g$ ($f + h$) is almost continuous in the sense of Stallings (does not have the Darboux property). Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 29-33. | ||||||||
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The space of the strong Świątkowski functions Joanna Kucner 1)
The definition of a strong Świątkowski property for a function $f : [a,b] ightarrow Bbb R$ at a fixed point of $[a,b]$ has been formulated in the paper [J. Kucner, R. J. Pawlak: On local characterization of the strong Świątkowski property for a function $f:[a,b ] ightarrow Bbb R$, Real Anal. Exchange 28 (2003), 563–572]. Theorem 11 presented in that paper seems to suggest the question connected with comparisons of the class of strong Świątkowski functions with the Baire class one. In this paper we give some answers to this question. In particular, we prove that in the space of bounded strong Świątkowski functions (with the metric of uniform convergence) a set $L$ of all functions measurable (in the Lebesgue sense) is a superporous set at each point of this space. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 35-42. | ||||||||
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A note on $σ$-discrete and massive spaces Stanislaw P. Ponomarev 1)
Some cardinality properties of $σ$-discrete and massive spaces are considered. These spaces were essentially used in the study of the problem on the existence of $ω$-primitives [Z. Dusyński, Z. Grande and S. P. Ponomarev: On the $ω$-primitive, Math. Slovaca 51 (2001), 469–476], [J. Ewert and S. P. Ponomarev: $ω$-primitives on $σ$-discrete metric spaces, Tatra Mt. Math. Publ. 24 (2002), 13–37], [J. Ewert and S. P. Ponomarev: On the existence of $ω$-primitives on arbitrary metric spaces, Math. Slovaca 3 (2003), 51–57], [J.Ewert and S. P. Ponomarev: Oscillation and $ω$-primitives, Real Anal. Exchange 26 (2001–2002), 687–702]. It is shown, in particular, that unlike metric spaces, a topological space which is not locally $σ$-discrete, need not contain a massive subspace. Moreover, a locally $σ$-discrete topological space need not be $σ$-discrete, and a massive topological space may contain a discrete subset of cardinality greater than the remaining set (in contrast with the case of metric spaces). Some other cardinality properties of the mentioned spaces, in particular under GCH or MA, are also discussed. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 43-56. | ||||||||
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On countably continuous functions Zbigniew Grande 1), Anna Fatz-Grupka 2)
A function $f:Bbb R o Bbb R$ is countably continuous if there are continuous functions $fn:Bbb R o Bbb R$ such that the graph of $f$ is contained in the union of the graphs of $fn$. We prove that the family of all countably continuous functions is closed with respect to the algebraic and lattice operations and that the superposition of two countably continuous functions is countably continuous. Moreover, we show some examples of monotone function and an approximately continuous function which are not countably continuous. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 57-63. | ||||||||
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Semi-quasicontinuity and PU–CHEN–PU theorem Grzegorz Szkibiel 1)
In connection with a widening of the Pu–Chen–Pu Theorem the four classes of semi-quasicontinuous functions are studied. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 65-70. | ||||||||
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On non-measurable unions of sections of a Borel set Ireneusz Recław 1)
Under Continuum Hypothesis we prove that for any Borel set on the plane with sections of measure zero and the union of all sections of positive outer measure there is a family of sections with non-measurable union. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 71-73. | ||||||||
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Rare and meager sets in relator spaces Arpad Szaz 1)
Rare and meager subsets of relator space are investigated. In particular, necessary and sufficient conditions the fat set be nonmeager are given. Since relator spaces are proper generalizations of not only uniform but also topological and closure spaces, the results obtained naturally extend, improve and supplement the corresponding results of former authors. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 75-95. | ||||||||
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Cardinal invariants ${frak p}$, ${frak t}$ and ${frak h}$ and real functions Michal Machura 1)
A partial order on a family of continuous functions from a topological space $X$ into $[ω]ω$ is defined as follows
$$ f subseteq* g iff f(x) subseteq*g (x) for any xin X. $$ For this order variants of cardinals ${frak p}$, ${frak t}$ and ${frak h}$ are defined and their values are estimated. | ||||||||
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Strong supmeasurability of functions of two variables Katarzyna Chmielewska 1)
We introduce and investigate the strong supmeasurability of functions of two variables. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 109-116. | ||||||||
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Sums of $Scr T<b>I$-quasi-continuous functions Katarzyna Flak 1), Ewa Łazarow 2), Aleksander Maliszewski 3)
For each finite family of cliquish functions $frak A$ we can find a Lebesgue function $α$ such that $f +α$ is strong Świątkowski and $Scr T<b>I$-quasi-continuous for every $fin frak A$. Consequently, each cliquish function is the sum of two $Scr T<b>I$-quasi-continuous strong Świątkowski functions. This result is a strengthened version of theorems proved earlier by H. W. Pu & H. H. Pu, Z. Grande, and A. Maliszewski, and it solves a problem posed by K. Flak. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 117-124. | ||||||||
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On measurable spaces and measurable maps Martin Papco 1)
We introduce and study the category ID the objects of which are suitable convergence D-posets of maps into the closed unit interval $I$ and the morphisms of which are sequentially continuous D-homomorphisms. We show that ID is dual to a subcategory of the category MID of generalized measurable spaces and generalized measurable maps. We construct epireflective and monocoreflective subcategories of ID and MID corresponding to two important properties of objects in ID, soberness and sequential closedness. The subcategories play important roles in applications to probability. We generalize some basic probability notions so that the generalized random variables are dual to generalized observables and generalized probability measures are ID-morphisms. Let $Iu$ be an ultrapower of $I$. We modify some of the previous results replacing $I$ by $Iu$ and replacing the sequential convergence by the approximation: a sequence approximates a point in $Iu$ whenever the sequence of standard parts converges to the standard part of the point in $I$. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 125-140. | ||||||||
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Note on the sup-measurability of multivalued functions Grażyna Kwiecińska 1)
For a multivalued function of two variables there is established a possibility of reinforcement of the conditions of measurability concerning the first variable and the conditions of semicontinuity concerning the second one that causes $F$ to be sup-measurable. Fulltext Tatra Mountains Mathematical Publications. Volume 28, 2004, No. 1: 141-151. |
