# H-closed extensions with countable remainder

Commentationes Mathematicae Universitatis Carolinae (2012)

- Volume: 53, Issue: 1, page 123-137
- ISSN: 0010-2628

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topMcNeill, Daniel K.. "H-closed extensions with countable remainder." Commentationes Mathematicae Universitatis Carolinae 53.1 (2012): 123-137. <http://eudml.org/doc/246731>.

@article{McNeill2012,

abstract = {This paper investigates necessary and sufficient conditions for a space to have an H-closed extension with countable remainder. For countable spaces we are able to give two characterizations of those spaces admitting an H-closed extension with countable remainder. The general case is more difficult, however, we arrive at a necessary condition — a generalization of Čech completeness, and several sufficient conditions for a space to have an H-closed extension with countable remainder. In particular, using the notation of Császár, we show that a space $X$ is a Čech $g$-space if and only if $X$ is $G_\delta $ in $\sigma X$ or equivalently if $EX$ is Čech complete. An example of a space which is a Čech $f$-space but not a Čech $g$-space is given answering a couple of questions of Császár. We show that if $X$ is a Čech $g$-space and $R(EX)$, the residue of $EX$, is Lindelöf, then $X$ has an H-closed extension with countable remainder. Finally, we investigate some natural generalizations of the residue to the class of all Hausdorff spaces.},

author = {McNeill, Daniel K.},

journal = {Commentationes Mathematicae Universitatis Carolinae},

keywords = {Čech complete; H-closed; extension; -closed space; remainder; countable space; Čech -space; Katetov space},

language = {eng},

number = {1},

pages = {123-137},

publisher = {Charles University in Prague, Faculty of Mathematics and Physics},

title = {H-closed extensions with countable remainder},

url = {http://eudml.org/doc/246731},

volume = {53},

year = {2012},

}

TY - JOUR

AU - McNeill, Daniel K.

TI - H-closed extensions with countable remainder

JO - Commentationes Mathematicae Universitatis Carolinae

PY - 2012

PB - Charles University in Prague, Faculty of Mathematics and Physics

VL - 53

IS - 1

SP - 123

EP - 137

AB - This paper investigates necessary and sufficient conditions for a space to have an H-closed extension with countable remainder. For countable spaces we are able to give two characterizations of those spaces admitting an H-closed extension with countable remainder. The general case is more difficult, however, we arrive at a necessary condition — a generalization of Čech completeness, and several sufficient conditions for a space to have an H-closed extension with countable remainder. In particular, using the notation of Császár, we show that a space $X$ is a Čech $g$-space if and only if $X$ is $G_\delta $ in $\sigma X$ or equivalently if $EX$ is Čech complete. An example of a space which is a Čech $f$-space but not a Čech $g$-space is given answering a couple of questions of Császár. We show that if $X$ is a Čech $g$-space and $R(EX)$, the residue of $EX$, is Lindelöf, then $X$ has an H-closed extension with countable remainder. Finally, we investigate some natural generalizations of the residue to the class of all Hausdorff spaces.

LA - eng

KW - Čech complete; H-closed; extension; -closed space; remainder; countable space; Čech -space; Katetov space

UR - http://eudml.org/doc/246731

ER -

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