English

QFS-space and its properties

General Topology 2022-12-14 v1

Abstract

In this paper, the concept of quasi-finitely separating map and quasiapproximate identity are introduced. Based on these concepts, QFS-spaces and quasicontinuous maps are defined. Properties and characterizations of QFS-spaces are explored. Main results are: (1) Each QFS-space is quasicontinuous space; (2) Closed subspaces, quasicontinuous projection spaces of QFS-spaces are QFS-spaces; (3) Continuous retracts of QFS-spaces are QFS-spaces and a kind of retracts of QFS-spaces are constructed; (4) Upper powerspaces of continuous QFS-spaces are FS-spaces.

Keywords

Cite

@article{arxiv.2211.10677,
  title  = {QFS-space and its properties},
  author = {Wu Wang},
  journal= {arXiv preprint arXiv:2211.10677},
  year   = {2022}
}

Comments

10 pages. arXiv admin note: substantial text overlap with arXiv:2211.08595

R2 v1 2026-06-28T06:16:13.756Z