A bornological approach to rotundity and smoothness applied to approximation.
It is well known that a function from a space into a space is continuous if and only if, for every set in the image of the closure of under is a subset of the closure of the image of it. In this paper we characterize almost continuity and weak continuity by proving similar relations for the subsets of .
Se ed sono spazi topologici, una funzione è detta regolarmente chiusa [5] se essa trasforma ogni insieme regolarmente chiuso di in un insieme chiuso di . Si dimostra che una funzione regolarmente chiusa risulta chiusa se è normale.
We provide an answer to a question: under what conditions almost continuity in the sense of Husain implies closure continuity?