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# $ls$-Ponomarev-systems and compact images of locally separable metric spaces

### Abstract

We introduce the notion of an $ls$-Ponomarev-system $(f, M, X, \{\mathcal{P}_{\lambda,n}\})$, and give necessary and sufficient conditions such that the mapping $f$ is a compact (compact-covering, sequence-covering, pseudo-sequence-covering, sequentially-quotient) mapping from a locally separable metric space $M$ onto a space $X$. As applications of these results, we systematically get characterizations of certain compact images of locally separable metric spaces.

### Article Information

 Title $ls$-Ponomarev-systems and compact images of locally separable metric spaces Source Methods Funct. Anal. Topology, Vol. 15 (2009), no. 4, 391-400 MathSciNet MR2603837 Copyright The Author(s) 2009 (CC BY-SA)

### Authors Information

Tran Van An
Department of Mathematics, Vinh University, Nghean Province, Vietnam

Nguyen Van Dung
Department of Mathematics, Pedagogical University of Dongthap, Dongthap Province, Vietnam

### Citation Example

Tran Van An and Nguyen Van Dung, $ls$-Ponomarev-systems and compact images of locally separable metric spaces, Methods Funct. Anal. Topology 15 (2009), no. 4, 391-400.

### BibTex

@article {MFAT497,
AUTHOR = {Tran Van An and Nguyen Van Dung},
TITLE = {$ls$-Ponomarev-systems and compact images of locally separable metric spaces},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {15},
YEAR = {2009},
NUMBER = {4},
PAGES = {391-400},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=497},
}