-continuity and closed graphs
C-closed functions
Characterizations of -Lindelöf spaces
A topological space is said to be -Lindelöf [1] if every cover of by cozero sets of admits a countable subcover. In this paper, we obtain new characterizations and preservation theorems of -Lindelöf spaces.
Characterizations of -stratifiable spaces
Classification of weak continuities and decomposition of continuity.
Connectedness and strong semicontinuity
Connectivity functions defined on
Connectivity of diagonal products of Baire one functions
We characterize those Baire one functions f for which the diagonal product x → (f(x), g(x)) has a connected graph whenever g is approximately continuous or is a derivative.
Continuity of semigroup actions.
Continuity properties up to a countable partition.
Approximation and rigidity properties in renorming constructions are characterized with some classes of simple maps. Those maps describe continuity properties up to a countable partition. The construction of such kind of maps can be done with ideas from the First Lebesgue Theorem. We present new results on the relationship between Kadec and locally uniformly rotund renormability as well as characterizations of the last one with the simple maps used here.
Continuous depencence of on as a selection property.
Contra--continuous and almost contra--continuous.
Contra-continuous functions and strongly -closed spaces.
Contra-pre-semi-continuous functions.
Contra-semicontinuous functions.