<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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 <italic>⊗</italic>R) is completely and strongly Hausdorff and that Q<italic>⊗</italic>Q is normal but not a <italic>p</italic>-space. In addition, we show that each point of Q <italic>⊗</italic>Q has an uncountable neighborhood base.</p></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 Q⊗Q is normal but not a p-space. In addition, we show that each point of Q ⊗Q has an uncountable neighborhood base.

On the separately open topology

Department of Mathematics Youngstown State University Youngstown, OH 44555 U.S.A.

Department of Mathematics Slippery Rock University of PA Slippery Rock, PA 16057 U.S.A.

Tatra Mountains Mathematical Publications

{"article-title":"On the separately open topology"}

We consider the relationship between separately continuous functions and separately open sets, and we study the properties of the separately open topology on...

On the separately open topology

Published Online: Nov 12, 2012

Page range: 39 - 49

DOI: https://doi.org/10.2478/v10127-009-0004-y

Keywords
separately open topology, separate continuity.

This content is open access.

On the separately open topology

Published Online: Nov 12, 2012

Page range: 39 - 49

DOI: https://doi.org/10.2478/v10127-009-0004-y

Keywordsseparately open topology, separate continuity.

This content is open access.

Keywords
separately open topology, separate continuity.