Compact images of spaces with a weaker metric topology

Title:

Compact images of spaces with a weaker metric topology

Creator:

Yan, Peng-Fei and Lü, Cheng

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:c6c492c4-9877-44ec-9fd5-f3adb68b41f5
uuid:c6c492c4-9877-44ec-9fd5-f3adb68b41f5

Subject:

sequence-covering mappings, sequentially-quotient mappings, compact mappings, and weaker metric topology

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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 $y\in Y$.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

921-926

Source:

Czechoslovak Mathematical Journal | 2008 Volume:58 | Number:4

Harvested from:

CDK

Metadata only:

false