Displaying similar documents to “On some results concerning k -spaces”

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

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

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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...

Moscow spaces, Pestov-Tkačenko Problem, and C -embeddings

Aleksander V. Arhangel'skii (2000)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

We show that there exists an Abelian topological group G such that the operations in G cannot be extended to the Dieudonné completion μ G of the space G in such a way that G becomes a topological subgroup of the topological group μ G . This provides a complete answer to a question of V.G. Pestov and M.G. Tkačenko, dating back to 1985. We also identify new large classes of topological groups for which such an extension is possible. The technique developed also allows to find many new solutions...