On relatively normal spaces, relatively regular spaces, and on relative property (a)

✍ Scribed by M.V. Matveev; O.I. Pavlov; J.K. Tartir

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 108 KB
• Volume: 93
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00265-4

✦ Synopsis

Spaces which have a certain relative topological property in every larger space from a certain class are investigated. It is proved that a regular (Tychonoff) space Y is normal in every larger regular (Tychonoff) space if and only if Y is Lindelöf or normal almost compact. A functionally Hausdorff space Y is regular in every larger functionally Hausdorff space if and only if Y is compact. A Hausdorff (regular, Tychonoff) space Y is relatively (a) in every larger Hausdorff (regular, Tychonoff) X if and only if Y is compact.