Compact images of spaces with a weaker metric topology

Peng-fei Yan; Cheng Lü

Czechoslovak Mathematical Journal (2008)

  • Volume: 58, Issue: 4, page 921-926
  • ISSN: 0011-4642

Abstract

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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 a sequentially-quotient 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 .

How to cite

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Yan, Peng-fei, and Lü, Cheng. "Compact images of spaces with a weaker metric topology." Czechoslovak Mathematical Journal 58.4 (2008): 921-926. <http://eudml.org/doc/37877>.

@article{Yan2008,
abstract = {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 $\lbrace \mathcal \{F\}_i\rbrace _\{i\in \mathbb \{N\}\}$ of point-finite $cs$-covers such that $ \{\bigcap _\{i\in \mathbb \{N\}\}\}\mathop \{\rm st\} (y,\mathcal \{F\}_i)=\lbrace y\rbrace $ for each $y\in Y$. (2) $Y$ is a sequentially-quotient compact image of a space with a weaker metric topology if and only if $Y$ has a sequence $\lbrace \mathcal \{F\}_i\rbrace _\{i\in \mathbb \{N\}\}$ of point-finite $cs^*$-covers such that $\{\bigcap _\{i\in \mathbb \{N\}\}\}\mathop \{\rm st\} (y,\mathcal \{F\}_i)=\lbrace y\rbrace $ for each $y\in Y$.},
author = {Yan, Peng-fei, Lü, Cheng},
journal = {Czechoslovak Mathematical Journal},
keywords = {sequence-covering mappings; sequentially-quotient mappings; compact mappings; weaker metric topology; sequence-covering mappings; sequentially-quotient mappings; compact mappings; weaker metric topology},
language = {eng},
number = {4},
pages = {921-926},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Compact images of spaces with a weaker metric topology},
url = {http://eudml.org/doc/37877},
volume = {58},
year = {2008},
}

TY - JOUR
AU - Yan, Peng-fei
AU - Lü, Cheng
TI - Compact images of spaces with a weaker metric topology
JO - Czechoslovak Mathematical Journal
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 58
IS - 4
SP - 921
EP - 926
AB - 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 $\lbrace \mathcal {F}_i\rbrace _{i\in \mathbb {N}}$ of point-finite $cs$-covers such that $ {\bigcap _{i\in \mathbb {N}}}\mathop {\rm st} (y,\mathcal {F}_i)=\lbrace y\rbrace $ for each $y\in Y$. (2) $Y$ is a sequentially-quotient compact image of a space with a weaker metric topology if and only if $Y$ has a sequence $\lbrace \mathcal {F}_i\rbrace _{i\in \mathbb {N}}$ of point-finite $cs^*$-covers such that ${\bigcap _{i\in \mathbb {N}}}\mathop {\rm st} (y,\mathcal {F}_i)=\lbrace y\rbrace $ for each $y\in Y$.
LA - eng
KW - sequence-covering mappings; sequentially-quotient mappings; compact mappings; weaker metric topology; sequence-covering mappings; sequentially-quotient mappings; compact mappings; weaker metric topology
UR - http://eudml.org/doc/37877
ER -

References

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