Note on limits of simply continuous and cliquish functions

Janina Ewert

International Journal of Mathematics and Mathematical Sciences, 1994, vol. 17, 1-4

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 { f n : n ≥ 1 } 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.

Date: 1994
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:507564

DOI: 10.1155/S0161171294000645

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