Function Spaces and Contractive Extensions in Approach Theory: The Role of Regularity Article First Online: 05 July 2013 Received: 25 January 2013 Accepted: 19 June 2013 DOI:
Cite this article as: Colebunders, E., Mynard, F. & Trott, W. Appl Categor Struct (2014) 22: 551. 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.
Keywords Regularity Strong regularity Convergence space Convergence-approach space Approach space Strict subspace Continuous extension Contractive extension Default of contraction Continuous convergence Diagonal axioms References
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