Displaying similar documents to “A proof for the Blair-Hager-Johnson theorem on absolute z -embedding”

On ℒ -starcompact spaces

Yan-Kui Song (2006)

Czechoslovak Mathematical Journal

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A space X is ℒ -starcompact if for every open cover 𝒰 of X , there exists a Lindelöf subset L of X such that S t ( L , 𝒰 ) = X . We clarify the relations between ℒ -starcompact spaces and other related spaces and investigate topological properties of ℒ -starcompact spaces. A question of Hiremath is answered.

Some relative properties on normality and paracompactness, and their absolute embeddings

Shinji Kawaguchi, Ryoken Sokei (2005)

Commentationes Mathematicae Universitatis Carolinae

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Paracompactness ( = 2 -paracompactness) and normality of a subspace Y in a space X defined by Arhangel’skii and Genedi [4] are fundamental in the study of relative topological properties ([2], [3]). These notions have been investigated by primary using of the notion of weak C - or weak P -embeddings, which are extension properties of functions defined in [2] or [18]. In fact, Bella and Yaschenko [8] characterized Tychonoff spaces which are normal in every larger Tychonoff space, and this result...

On AP spaces in concern with compact-like sets and submaximality

Mi Ae Moon, Myung Hyun Cho, Junhui Kim (2011)

Commentationes Mathematicae Universitatis Carolinae

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The definitions of AP and WAP were originated in categorical topology by A. Pultr and A. Tozzi, Equationally closed subframes and representation of quotient spaces, Cahiers Topologie Géom. Différentielle Catég. 34 (1993), no. 3, 167-183. In general, we have the implications: T 2 ⇒ K C ⇒ U S ⇒ T 1 , where K C is defined as the property that every compact subset is closed and U S is defined as the property that every convergent sequence has at most one limit. And a space is called submaximal if every dense subset...