# $\pi $-mappings in $ls$-Ponomarev-systems

## Nguyen Van Dung

Address: Mathematics Faculty, Dongthap University, Caolanh City, Dongthap Province, Vietnam

E-mail:

nvdung@staff.dthu.edu.vn

nguyendungtc@yahoo.com

Abstract: We use the $ls$-Ponomarev-system $(f, M, X, \lbrace \mathcal{P}_{\lambda ,n}\rbrace )$, where $M$ is a locally separable metric space, to give a consistent method to construct a $\pi $-mapping (compact mapping) with covering-properties from a locally separable metric space $M$ onto a space $X$. As applications of these results, we systematically get characterizations of certain $\pi $-images (compact images) of locally separable metric spaces.

AMSclassification: primary 54E40; secondary 54E99.

Keywords: sequence-covering, compact-covering, pseudo-sequence-covering, sequentially-quotient, \pi -mapping, ls-Ponomarev-system, double point-star cover.