International Journal of Mathematics and Mathematical Sciences
Volume 17 (1994), Issue 3, Pages 447-450
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 Janina Ewert. 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.
The main result of this paper is that any function defined on a perfect Baire space with values in a separable metric space is cliquish (has the Baire property) iff it is a uniform (pointwise) limit of sequence of simply continuous functions. This result is obtained by a change of a topology on and showing that a function is cliquish (has the Baire property) iff it is of the Baire class 1 (class 2) with respect to the new topology.