Mappings and Spaces Defined by the Function Epsilon
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.
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
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)
Article - Journal
© 2021 Elsevier, All rights reserved.
15 Aug 2021