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Remarks on sequence-covering maps

Luong Quoc Tuyen (2012)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we prove that each sequence-covering and boundary-compact map on g -metrizable spaces is 1-sequence-covering. Then, we give some relationships between sequence-covering maps and 1-sequence-covering maps or weak-open maps, and give an affirmative answer to the problem posed by F.C. Lin and S. Lin in [Lin.F.C.and.Lin.S-2011].

Remarks on strongly star-Menger spaces

Yan-Kui Song (2013)

Commentationes Mathematicae Universitatis Carolinae

A space X is strongly star-Menger if for each sequence ( 𝒰 n : n ) of open covers of X , there exists a sequence ( K n : n N ) of finite subsets of X such that { S t ( K n , 𝒰 n ) : n } is an open cover of X . In this paper, we investigate the relationship between strongly star-Menger spaces and related spaces, and also study topological properties of strongly star-Menger spaces.

Rétractes Absolus de Voisinage Algébriques

Cauty, Robert (2005)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 54C55, 54H25, 55M20.We introduce the class of algebraic ANRs. It is defined by replacing continuous maps by chain mappings in Lefschetz’s characterization of ANRs. To a large extent, the theory of algebraic ANRs parallels the classical theory of ANRs. Every ANR is an algebraic ANR, but the class of algebraic ANRs is much larger; the most striking difference between these classes is that every locally equiconnected metrisable space is an algebraic ANR, whereas...

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