Mappings and Spaces Defined by the Function Epsilon

Author

W. J. Charatonik, Missouri University of Science and TechnologyFollow
Daria Michalik

Abstract

The function εX assigns to each point of a given continuum X the closure of the family of all continua that contain x in their interior. We define the class S(ε) of continua for which the function εX is continuous. On the other hand, we consider some natural diagram involving the function εX and commutativity of this diagram defines a class of mappings M(ε). We investigate classes S(ε) and M(ε), and relations between them.

Recommended Citation

W. J. Charatonik and D. Michalik, "Mappings and Spaces Defined by the Function Epsilon," Topology and its Applications, vol. 300, article no. 107741, Elsevier, Aug 2021.

The definitive version is available at https://doi.org/10.1016/j.topol.2021.107741

Department(s)

Mathematics and Statistics

Keywords and Phrases

Confluent Map; Continuum; Kelley Property; Lower Semi-Continuous Function; Set-Valued Function; Upper Semi-Continuous Function

International Standard Serial Number (ISSN)

0166-8641

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2021 Elsevier, All rights reserved.

Publication Date

15 Aug 2021