Continuity properties of functions. (English) Zbl 0605.54011

Gauld, D. B.; Mršević, M.; Reilly, I. L.; Vamanamurthy, M. K.

Topology theory and applications, 5th Colloq., Eger/Hung. 1983, Colloq. Math. Soc. János Bolyai 41, 311-322 (1985).

[For the entire collection see Zbl 0588.00022.]
The authors call a property P of functions between topological spaces \((X,\zeta)\) and \((Y,\eta)\) an \(\iota\)-continuity (respectively \(\phi\)- continuity; \(\mu\)-continuity) property if there is a function \(\alpha\) which assigns to each topology U a topology \(\alpha\) (U) on the same underlying set such that \(f: (X,\zeta)\to (Y,\eta)\) has property P if and only if \(f: (X,\alpha(\zeta)) \to (Y,\eta)\) (respectively \(f: (X,\zeta) \to (Y,\alpha(\eta))\); \(f: (X,\alpha(\zeta)) \to (Y,\alpha (\eta))\) is continuous. Then they give many examples of such continuous properties. Finally they show that some properties of functions are not continuity properties.

Reviewer: D.C.Demaria

MSC:

54C08

Weak and generalized continuity

Citations:

Zbl 0588.00022