Displaying similar documents to “A note on ℵ -spaces and g -metrizable spaces”

Notes on c f p -covers

Shou Lin, Peng Fei Yan (2003)

Commentationes Mathematicae Universitatis Carolinae

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The main purpose of this paper is to establish general conditions under which T 2 -spaces are compact-covering images of metric spaces by using the concept of c f p -covers. We generalize a series of results on compact-covering open images and sequence-covering quotient images of metric spaces, and correct some mapping characterizations of g -metrizable spaces by compact-covering σ -maps and m s s c -maps.

g -metrizable spaces and the images of semi-metric spaces

Ying Ge, Shou Lin (2007)

Czechoslovak Mathematical Journal

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In this paper, we prove that a space X is a g -metrizable space if and only if X is a weak-open, π and σ -image of a semi-metric space, if and only if X is a strong sequence-covering, quotient, π and m s s c -image of a semi-metric space, where “semi-metric” can not be replaced by “metric”.

A note on g -metrizable spaces

Jinjin Li (2003)

Czechoslovak Mathematical Journal

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In this paper, the relationships between metric spaces and g -metrizable spaces are established in terms of certain quotient mappings, which is an answer to Alexandroff’s problems.

Compact images of spaces with a weaker metric topology

Peng-fei Yan, Cheng Lü (2008)

Czechoslovak Mathematical Journal

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If X is a space that can be mapped onto a metric space by a one-to-one mapping, then X is said to have a weaker metric topology. In this paper, we give characterizations of sequence-covering compact images and sequentially-quotient compact images of spaces with a weaker metric topology. The main results are that (1) Y is a sequence-covering compact image of a space with a weaker metric topology if and only if Y has a sequence { ℱ i } i ∈ ℕ of point-finite c s -covers such that ⋂ i ∈ ℕ st ( y , ℱ i ) = { y } for each y ∈ Y . (2) Y is...