Countably z-compact spaces
Archivum Mathematicum (2014)
- Volume: 050, Issue: 2, page 97-100
- ISSN: 0044-8753
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topAl-Ani, A.T.. "Countably z-compact spaces." Archivum Mathematicum 050.2 (2014): 97-100. <http://eudml.org/doc/261181>.
@article{Al2014,
abstract = {In this work we study countably z-compact spaces and z-Lindelof spaces. Several new properties of them are given. It is proved that every countably z-compact space is pseuodocompact (a space on which every real valued continuous function is bounded). Spaces which are countably z-compact but not countably compact are given. It is proved that a space is countably z-compact iff every countable z-closed set is compact. Characterizations of countably z-compact and z-Lindelof spaces by multifunctions are given.},
author = {Al-Ani, A.T.},
journal = {Archivum Mathematicum},
keywords = {z-compact space; z-Lindelof space; compact space; pseudocompact space; realcompact space; z-compact space; z-Lindelöf space; compact space; pseudocompact space; realcompact space},
language = {eng},
number = {2},
pages = {97-100},
publisher = {Department of Mathematics, Faculty of Science of Masaryk University, Brno},
title = {Countably z-compact spaces},
url = {http://eudml.org/doc/261181},
volume = {050},
year = {2014},
}
TY - JOUR
AU - Al-Ani, A.T.
TI - Countably z-compact spaces
JO - Archivum Mathematicum
PY - 2014
PB - Department of Mathematics, Faculty of Science of Masaryk University, Brno
VL - 050
IS - 2
SP - 97
EP - 100
AB - In this work we study countably z-compact spaces and z-Lindelof spaces. Several new properties of them are given. It is proved that every countably z-compact space is pseuodocompact (a space on which every real valued continuous function is bounded). Spaces which are countably z-compact but not countably compact are given. It is proved that a space is countably z-compact iff every countable z-closed set is compact. Characterizations of countably z-compact and z-Lindelof spaces by multifunctions are given.
LA - eng
KW - z-compact space; z-Lindelof space; compact space; pseudocompact space; realcompact space; z-compact space; z-Lindelöf space; compact space; pseudocompact space; realcompact space
UR - http://eudml.org/doc/261181
ER -
References
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- Gillman, L., Jerison, M., Rings of continuous functions, University Series in Higher Mathematics, Springer-Verlag, 1960. (1960) Zbl0093.30001MR0116199
- Kirch, A.M., 10.2307/2317265, Amer. Math. Monthly 76 (1969), 169–171. (1969) Zbl0174.25602MR0239563DOI10.2307/2317265
- Kohli, J.K., Quasi z-supercontinuous and pseudo z-supercontinuous functions, Stud. Cercet. Ştiinţ. Ser. Mat. Univ. Bacău 14 (2004) (2005), 43–56. (2005) MR2239863
- Steen, L.A., Seebach, J. A., Jr.,, Counterexamples in Topology, second ed., Springer-Verlag, 1978. (1978) Zbl0386.54001MR0507446
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