THE $\sigma$-POINT-FINITE $cn$-NETWORKS ($ck$-NETWORKS) OF PIXLEY-ROY HYPERSPACES

Authors

  • L. Q. Tuyen Department of Mathematics, Da Nang University of Education, 459 Ton Duc Thang Street, Da Nang City, Vietnam Author
  • O. V. Tuyen Hoa Vang High School, 101 Ong Ich Duong Street, Da Nang City, Vietnam Author

DOI:

https://doi.org/10.57016/MV-woXu7919

Keywords:

Pixley-Roy, hyperspace, $cn$-network, $ck$-network, $\sigma$-point-finite

Subjects:

54B20, 54D20

Abstract

In this paper, we study the relation between a space $X$ satisfying certain generalized metric properties and the Pixley-Roy hyperspace $\mathcal F[X]$ over $X$ satisfying the same properties. We prove that if $X$ has a $\sigma$-point-finite $cn$-network (resp., $ck$-network), then $\mathcal F[X]$ also has a $\sigma$-point-finite $cn$-network (resp., $ck$-network).

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Published

2023-04-15

Issue

Vol. 75 No. 2 (2023): Vol. 75, Issue 2

Section

Articles

License

Copyright (c) 2023 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.