Function Spaces and Contractive Extensions in Approach Theory: The Role of Regularity
Applied Categorical Structures
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.
Colebunders, Eva, Frédéric D. Mynard, William Trott.
"Function Spaces and Contractive Extensions in Approach Theory: The Role of Regularity."
Applied Categorical Structures, 22 (3): 551-563.