Geodesic
Compact images of spaces with a weaker metric topology
Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 921-926 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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. \endgraf 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 \endgraf (1) $Y$ is a sequence-covering compact image of a space with a weaker metric topology if and only if $Y$ has a sequence $\{\mathcal F_i\}_{i\in \mathbb N}$ of point-finite $cs$-covers such that $ {\bigcap _{i\in \mathbb N}}\mathop{\rm st} (y,\mathcal F_i)=\{y\}$ for each $y\in Y$. \endgraf (2) $Y$ is a sequentially-quotient compact image of a space with a weaker metric topology if and only if $Y$ has a sequence $\{\mathcal F_i\}_{i\in \mathbb N}$ of point-finite $cs^*$-covers such that ${\bigcap _{i\in \mathbb N}}\mathop{\rm st} (y,\mathcal F_i)=\{y\}$ for each $y\in Y$.
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. \endgraf 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 \endgraf (1) $Y$ is a sequence-covering compact image of a space with a weaker metric topology if and only if $Y$ has a sequence $\{\mathcal F_i\}_{i\in \mathbb N}$ of point-finite $cs$-covers such that $ {\bigcap _{i\in \mathbb N}}\mathop{\rm st} (y,\mathcal F_i)=\{y\}$ for each $y\in Y$. \endgraf (2) $Y$ is a sequentially-quotient compact image of a space with a weaker metric topology if and only if $Y$ has a sequence $\{\mathcal F_i\}_{i\in \mathbb N}$ of point-finite $cs^*$-covers such that ${\bigcap _{i\in \mathbb N}}\mathop{\rm st} (y,\mathcal F_i)=\{y\}$ for each $y\in Y$.
Classification : 54C10, 54C40, 54E99
Keywords: sequence-covering mappings; sequentially-quotient mappings; compact mappings; weaker metric topology 
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}
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Yan, Peng-fei; Lü, Cheng. Compact images of spaces with a weaker metric topology. Czechoslovak Mathematical Journal, Tome 58 (2008) no. 4, pp. 921-926. http://geodesic.mathdoc.fr/item/CMJ_2008_58_4_a4/

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