Geodesic
Countably z-compact spaces
Archivum mathematicum, Tome 50 (2014) no. 2, pp. 97-100
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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.
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.
DOI : 10.5817/AM2014-2-97
Classification : 54C60, 54D30, 54D35
Keywords: z-compact space; z-Lindelof space; compact space; pseudocompact space; realcompact space 
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Al-Ani, A.T. Countably z-compact spaces. Archivum mathematicum, Tome 50 (2014) no. 2, pp. 97-100. doi: 10.5817/AM2014-2-97

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