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Quasicontinuous functions, minimal USCO maps and topology of pointwise convergence

In: Mathematica Slovaca, vol. 60, no. 4
Dušan Holý - Ladislav Matejíčka
Detaily:
Rok, strany: 2010, 507 - 520
Kľúčové slová:
quasicontinuous function, locally bounded function, minimal USCO map, upper semicontinuous function, topology of pointwise convergence
O článku:
In [HOLÁ, Ľ.---HOLÝ, D.: \textit{Pointwise convergence of quasicontinuous mappings and Baire spaces}, Rocky Mountain J. Math.] a complete answer is given, for a Baire space $X$, to the question of when the pointwise limit of a sequence of real-valued quasicontinuous functions defined on $X$ is quasicontinuous. In [HOLÁ, Ľ.---HOLÝ, D.: \textit{Minimal USCO maps, densely continuous forms and upper semicontinuous functions}, Rocky Mountain J. Math. \textbf{39} (2009), 545--562], a characterization of minimal USCO maps by quasicontinuous and subcontinuous selections is proved. Continuing these results, we study closed and compact subsets of the space of quasicontinuous functions and minimal USCO maps equipped with the topology of pointwise convergence. We also study conditions under which the closure of the graph of a set-valued mapping which is the pointwise limit of a net of set-valued mappings, is a minimal USCO map.
Ako citovať:
ISO 690:
Holý, D., Matejíčka, L. 2010. Quasicontinuous functions, minimal USCO maps and topology of pointwise convergence. In Mathematica Slovaca, vol. 60, no.4, pp. 507-520. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0029-3

APA:
Holý, D., Matejíčka, L. (2010). Quasicontinuous functions, minimal USCO maps and topology of pointwise convergence. Mathematica Slovaca, 60(4), 507-520. 0139-9918. DOI: https://doi.org/10.2478/s12175-010-0029-3
O vydaní: