On AP and WAP spaces

Angelo Bella; Ivan V. Yashchenko

Commentationes Mathematicae Universitatis Carolinae (1999)

  • Volume: 40, Issue: 3, page 531-536
  • ISSN: 0010-2628

Abstract

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Several remarks on the properties of approximation by points (AP) and weak approximation by points (WAP) are presented. We look in particular at their behavior in product and at their relationships with radiality, pseudoradiality and related concepts. For instance, relevant facts are: (a) There is in ZFC a product of a countable WAP space with a convergent sequence which fails to be WAP. (b) C p over σ -compact space is AP. Therefore AP does not imply even pseudoradiality in function spaces, while it implies Fréchet-Urysohn property in compact spaces. (c) WAP and AP do not coincide in C p .

How to cite

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Bella, Angelo, and Yashchenko, Ivan V.. "On AP and WAP spaces." Commentationes Mathematicae Universitatis Carolinae 40.3 (1999): 531-536. <http://eudml.org/doc/248404>.

@article{Bella1999,
abstract = {Several remarks on the properties of approximation by points (AP) and weak approximation by points (WAP) are presented. We look in particular at their behavior in product and at their relationships with radiality, pseudoradiality and related concepts. For instance, relevant facts are: (a) There is in ZFC a product of a countable WAP space with a convergent sequence which fails to be WAP. (b) $C_p$ over $\sigma $-compact space is AP. Therefore AP does not imply even pseudoradiality in function spaces, while it implies Fréchet-Urysohn property in compact spaces. (c) WAP and AP do not coincide in $C_p$.},
author = {Bella, Angelo, Yashchenko, Ivan V.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {AP space; WAP space; pseudoradial space; radial space; product; compact space; submaximal space; function space; radial space; function space},
language = {eng},
number = {3},
pages = {531-536},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On AP and WAP spaces},
url = {http://eudml.org/doc/248404},
volume = {40},
year = {1999},
}

TY - JOUR
AU - Bella, Angelo
AU - Yashchenko, Ivan V.
TI - On AP and WAP spaces
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1999
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 40
IS - 3
SP - 531
EP - 536
AB - Several remarks on the properties of approximation by points (AP) and weak approximation by points (WAP) are presented. We look in particular at their behavior in product and at their relationships with radiality, pseudoradiality and related concepts. For instance, relevant facts are: (a) There is in ZFC a product of a countable WAP space with a convergent sequence which fails to be WAP. (b) $C_p$ over $\sigma $-compact space is AP. Therefore AP does not imply even pseudoradiality in function spaces, while it implies Fréchet-Urysohn property in compact spaces. (c) WAP and AP do not coincide in $C_p$.
LA - eng
KW - AP space; WAP space; pseudoradial space; radial space; product; compact space; submaximal space; function space; radial space; function space
UR - http://eudml.org/doc/248404
ER -

References

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