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International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 3, Pages 447-450
http://dx.doi.org/10.1155/S0161171294000645

Note on limits of simply continuous and cliquish functions

Department of Mathematics, Pedagogical University, Arciszewskiego 22, Słupsk 76-200, Poland

Received 18 May 1992; Revised 14 June 1993

Copyright © 1994 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The main result of this paper is that any function f defined on a perfect Baire space (X,T) with values in a separable metric space Y is cliquish (has the Baire property) iff it is a uniform (pointwise) limit of sequence {fn:n1} of simply continuous functions. This result is obtained by a change of a topology on X and showing that a function f:(X,T)Y is cliquish (has the Baire property) iff it is of the Baire class 1 (class 2) with respect to the new topology.