Title

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

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.

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