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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 [].

About w c s -covers and w c s * -networks on the Vietoris hyperspace ( X )

Luong Quoc TuyenOng V. TuyenPhan D. TuanNguzen X. Truc — 2023

Commentationes Mathematicae Universitatis Carolinae

We study some generalized metric properties on the hyperspace ( X ) of finite subsets of a space X endowed with the Vietoris topology. We prove that X has a point-star network consisting of (countable) w c s -covers if and only if so does ( X ) . Moreover, X has a sequence of w c s -covers with property ( P ) which is a point-star network if and only if so does ( X ) , where ( P ) is one of the following properties: point-finite, point-countable, compact-finite, compact-countable, locally finite, locally countable. On the other...

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