On the separately open topology

Author:

Piotrowski Zbigniew,Vallin Robert W.,Wingler Eric

Abstract

Abstract We consider the relationship between separately continuous functions and separately open sets, and we study the properties of the separately open topology on R2 and on Q2. We show that R2 with this topology (denoted R R) is completely and strongly Hausdorff and that QQ is normal but not a p-space. In addition, we show that each point of Q Q has an uncountable neighborhood base.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

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