On a question of C c ( X )

A. R. Olfati

Commentationes Mathematicae Universitatis Carolinae (2016)

  • Volume: 57, Issue: 2, page 253-260
  • ISSN: 0010-2628

Abstract

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In this short article we answer the question posed in Ghadermazi M., Karamzadeh O.A.S., Namdari M., On the functionally countable subalgebra of C ( X ) , Rend. Sem. Mat. Univ. Padova 129 (2013), 47–69. It is shown that C c ( X ) is isomorphic to some ring of continuous functions if and only if υ 0 X is functionally countable. For a strongly zero-dimensional space X , this is equivalent to say that X is functionally countable. Hence for every P -space it is equivalent to pseudo- ℵ 0 -compactness.

How to cite

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Olfati, A. R.. "On a question of $C_c(X)$." Commentationes Mathematicae Universitatis Carolinae 57.2 (2016): 253-260. <http://eudml.org/doc/280142>.

@article{Olfati2016,
abstract = {In this short article we answer the question posed in Ghadermazi M., Karamzadeh O.A.S., Namdari M., On the functionally countable subalgebra of $C(X)$, Rend. Sem. Mat. Univ. Padova 129 (2013), 47–69. It is shown that $C_c(X)$ is isomorphic to some ring of continuous functions if and only if $\upsilon _0 X$ is functionally countable. For a strongly zero-dimensional space $X$, this is equivalent to say that $X$ is functionally countable. Hence for every $P$-space it is equivalent to pseudo-$\aleph _0$-compactness.},
author = {Olfati, A. R.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {zero-dimensional space; strongly zero-dimensional space; $\mathbb \{N\}$-compact space; Banaschewski compactification; character; ring homomorphism; functionally countable subring; functional separability},
language = {eng},
number = {2},
pages = {253-260},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On a question of $C_c(X)$},
url = {http://eudml.org/doc/280142},
volume = {57},
year = {2016},
}

TY - JOUR
AU - Olfati, A. R.
TI - On a question of $C_c(X)$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2016
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 57
IS - 2
SP - 253
EP - 260
AB - In this short article we answer the question posed in Ghadermazi M., Karamzadeh O.A.S., Namdari M., On the functionally countable subalgebra of $C(X)$, Rend. Sem. Mat. Univ. Padova 129 (2013), 47–69. It is shown that $C_c(X)$ is isomorphic to some ring of continuous functions if and only if $\upsilon _0 X$ is functionally countable. For a strongly zero-dimensional space $X$, this is equivalent to say that $X$ is functionally countable. Hence for every $P$-space it is equivalent to pseudo-$\aleph _0$-compactness.
LA - eng
KW - zero-dimensional space; strongly zero-dimensional space; $\mathbb {N}$-compact space; Banaschewski compactification; character; ring homomorphism; functionally countable subring; functional separability
UR - http://eudml.org/doc/280142
ER -

References

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