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Function spaces and contractive extensions in approach theory, the role of regularity

Journal Contribution - Journal Article

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.
Journal: Appl. Categ. Struct.
ISSN: 0927-2852
Issue: DOI 10.1007/s10485-013-9321-z
Volume: 22
Pages: 551-563
Publication year:2014
Keywords:Regularity, Approach space, Contractive extension
  • Scopus Id: 84904267400