An independency result in connectification theory

Alessandro Fedeli; Attilio Le Donne

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 2, page 331-334
  • ISSN: 0010-2628

Abstract

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A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let ψ be the following statement: “a perfect T 3 -space X with no more than 2 𝔠 clopen subsets is connectifiable if and only if no proper nonempty clopen subset of X is feebly compact". In this note we show that neither ψ nor ¬ ψ is provable in ZFC.

How to cite

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Fedeli, Alessandro, and Le Donne, Attilio. "An independency result in connectification theory." Commentationes Mathematicae Universitatis Carolinae 40.2 (1999): 331-334. <http://eudml.org/doc/248414>.

@article{Fedeli1999,
abstract = {A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let $\psi $ be the following statement: “a perfect $T_3$-space $X$ with no more than $2^\{\mathfrak \{c\}\}$ clopen subsets is connectifiable if and only if no proper nonempty clopen subset of $X$ is feebly compact". In this note we show that neither $\psi $ nor $\lnot \psi $ is provable in ZFC.},
author = {Fedeli, Alessandro, Le Donne, Attilio},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {connectifiable; perfect; feebly compact; connectifiable; perfect; feebly compact},
language = {eng},
number = {2},
pages = {331-334},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {An independency result in connectification theory},
url = {http://eudml.org/doc/248414},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Fedeli, Alessandro
AU - Le Donne, Attilio
TI - An independency result in connectification theory
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 2
SP - 331
EP - 334
AB - A space is called connectifiable if it can be densely embedded in a connected Hausdorff space. Let $\psi $ be the following statement: “a perfect $T_3$-space $X$ with no more than $2^{\mathfrak {c}}$ clopen subsets is connectifiable if and only if no proper nonempty clopen subset of $X$ is feebly compact". In this note we show that neither $\psi $ nor $\lnot \psi $ is provable in ZFC.
LA - eng
KW - connectifiable; perfect; feebly compact; connectifiable; perfect; feebly compact
UR - http://eudml.org/doc/248414
ER -

References

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  11. Swardson M.A., Nearly realcompact spaces and T 2 -connectifiability, 358-361 Proceedings of the 8th Prague Topological Symposium (1996). (1996) MR1617114
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