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A note on g -metrizable spaces

Jinjin Li (2003)

Czechoslovak Mathematical Journal

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.

A note on -spaces and g -metrizable spaces

Zhaowen Li (2005)

Czechoslovak Mathematical Journal

In this paper, we give the mapping theorems on -spaces and g -metrizable spaces by means of some sequence-covering mappings, mssc-mappings and π -mappings.

A note on topological groups and their remainders

Liang-Xue Peng, Yu-Feng He (2012)

Czechoslovak Mathematical Journal

In this note we first give a summary that on property of a remainder of a non-locally compact topological group G in a compactification b G makes the remainder and the topological group G all separable and metrizable. If a non-locally compact topological group G has a compactification b G such that the remainder b G G of G belongs to 𝒫 , then G and b G G are separable and metrizable, where 𝒫 is a class of spaces which satisfies the following conditions: (1) if X 𝒫 , then every compact subset of the space X is a...

Coarea integration in metric spaces

Malý, Jan (2003)

Nonlinear Analysis, Function Spaces and Applications

Let X be a metric space with a doubling measure, Y be a boundedly compact metric space and u : X Y be a Lebesgue precise mapping whose upper gradient g belongs to the Lorentz space L m , 1 , m 1 . Let E X be a set of measure zero. Then ^ m ( E u - 1 ( y ) ) = 0 for m -a.e. y Y , where m is the m -dimensional Hausdorff measure and ^ m is the m -codimensional Hausdorff measure. This property is closely related to the coarea formula and implies a version of the Eilenberg inequality. The result relies on estimates of Hausdorff content of level sets...

Compact images of spaces with a weaker metric topology

Peng-fei Yan, Cheng Lü (2008)

Czechoslovak Mathematical Journal

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 { i } i of point-finite c s -covers such that i st ( y , i ) = { y } for each y Y . (2) Y is a sequentially-quotient...

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