Functional characterizations of p-spaces

Ľubica Holá

Open Mathematics (2013)

  • Volume: 11, Issue: 12, page 2197-2202
  • ISSN: 2391-5455

Abstract

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We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.

How to cite

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Ľubica Holá. "Functional characterizations of p-spaces." Open Mathematics 11.12 (2013): 2197-2202. <http://eudml.org/doc/269007>.

@article{ĽubicaHolá2013,
abstract = {We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.},
author = {Ľubica Holá},
journal = {Open Mathematics},
keywords = {p-space; Čech-complete space; p-embedded; Extension of a function; Quasicontinuous function; Subcontinuous function; -space; -embedded; extension of a function; quasicontinuous function; subcontinuous function},
language = {eng},
number = {12},
pages = {2197-2202},
title = {Functional characterizations of p-spaces},
url = {http://eudml.org/doc/269007},
volume = {11},
year = {2013},
}

TY - JOUR
AU - Ľubica Holá
TI - Functional characterizations of p-spaces
JO - Open Mathematics
PY - 2013
VL - 11
IS - 12
SP - 2197
EP - 2202
AB - We show that a completely regular space Y is a p-space (a Čech-complete space, a locally compact space) if and only if given a dense subspace A of any topological space X and a continuous f: A → Y there are a p-embedded subset (resp. a G δ-subset, an open subset) M of X containing A and a quasicontinuous subcontinuous extension f*: M → Y of f continuous at every point of A. A result concerning a continuous extension to a residual set is also given.
LA - eng
KW - p-space; Čech-complete space; p-embedded; Extension of a function; Quasicontinuous function; Subcontinuous function; -space; -embedded; extension of a function; quasicontinuous function; subcontinuous function
UR - http://eudml.org/doc/269007
ER -

References

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