Base-base paracompactness and subsets of the Sorgenfrey line

Strashimir G. Popvassilev

Mathematica Bohemica (2012)

  • Volume: 137, Issue: 4, page 395-401
  • ISSN: 0862-7959

Abstract

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A topological space X is called base-base paracompact (John E. Porter) if it has an open base ℬ such that every base ℬ ' ⊆ ℬ has a locally finite subcover 𝒞 ⊆ ℬ ' . It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.

How to cite

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Popvassilev, Strashimir G.. "Base-base paracompactness and subsets of the Sorgenfrey line." Mathematica Bohemica 137.4 (2012): 395-401. <http://eudml.org/doc/246244>.

@article{Popvassilev2012,
abstract = {A topological space $X$ is called base-base paracompact (John E. Porter) if it has an open base $\mathcal \{B\}$ such that every base $\{\mathcal \{B\}^\{\prime \} \subseteq \mathcal \{B\}\}$ has a locally finite subcover $\mathcal \{C\} \subseteq \mathcal \{B\}^\{\prime \}$. It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.},
author = {Popvassilev, Strashimir G.},
journal = {Mathematica Bohemica},
keywords = {base-base paracompact space; coarse base; Sorgenfrey irrationals; totally imperfect set; base-base paracompact space; coarse base; Sorgenfrey irrationals; totally imperfect set},
language = {eng},
number = {4},
pages = {395-401},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Base-base paracompactness and subsets of the Sorgenfrey line},
url = {http://eudml.org/doc/246244},
volume = {137},
year = {2012},
}

TY - JOUR
AU - Popvassilev, Strashimir G.
TI - Base-base paracompactness and subsets of the Sorgenfrey line
JO - Mathematica Bohemica
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 137
IS - 4
SP - 395
EP - 401
AB - A topological space $X$ is called base-base paracompact (John E. Porter) if it has an open base $\mathcal {B}$ such that every base ${\mathcal {B}^{\prime } \subseteq \mathcal {B}}$ has a locally finite subcover $\mathcal {C} \subseteq \mathcal {B}^{\prime }$. It is not known if every paracompact space is base-base paracompact. We study subspaces of the Sorgenfrey line (e.g. the irrationals, a Bernstein set) as a possible counterexample.
LA - eng
KW - base-base paracompact space; coarse base; Sorgenfrey irrationals; totally imperfect set; base-base paracompact space; coarse base; Sorgenfrey irrationals; totally imperfect set
UR - http://eudml.org/doc/246244
ER -

References

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