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A characterization of almost continuity and weak continuity

Chrisostomos Petalas, Theodoros Vidalis (2004)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

It is well known that a function f from a space X into a space Y is continuous if and only if, for every set K in X the image of the closure of K under f 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 K of X .

A Note on Regular-closed Functions

Takashi Noiri (1981)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

Se X ed Y sono spazi topologici, una funzione f : X Y è detta regolarmente chiusa [5] se essa trasforma ogni insieme regolarmente chiuso di X in un insieme chiuso di Y . Si dimostra che una funzione regolarmente chiusa f : X Y risulta chiusa se X è normale.

Almost continuity vs closure continuity

B. A. Saleemi, Naseer Shahzad, M. A. Alghamdi (2001)

Archivum Mathematicum

We provide an answer to a question: under what conditions almost continuity in the sense of Husain implies closure continuity?

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