Function Spaces and Contractive Extensions in Approach Theory: The Role of Regularity

Authors

Eva Colebunders, Vrije Universiteit Brussel
Frédéric D. Mynard, Georgia Southern UniversityFollow
William Trott, Universidade de Aveiro

Document Type

Article

Publication Date

6-2014

Publication Title

Applied Categorical Structures

DOI

10.1007/s10485-013-9321-z

Abstract

Two classical results characterizing regularity of a convergence space in terms of continuous extensions of maps on one hand, and in terms of continuity of limits for the continuous convergence on the other, are extended to convergence-approach spaces. Characterizations are obtained for two alternative extensions of regularity to convergence-approach spaces: regularity and strong regularity. The results improve upon what is known even in the convergence case. On the way, a new notion of strictness for convergence-approach spaces is introduced.

Recommended Citation

Colebunders, Eva, Frédéric D. Mynard, William Trott. 2014. "Function Spaces and Contractive Extensions in Approach Theory: The Role of Regularity." Applied Categorical Structures, 22 (3): 551-563. doi: 10.1007/s10485-013-9321-z
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/271