On the separately open topology

Zbigniew Piotrowski; Robert W. Vallin; Eric Wingler

doi:10.2478/v10127-009-0004-y

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On the separately open topology

Tatra Mountains Mathematical Publications

Volume 42 (2009): Issue 1 (April 2009)

By: Zbigniew Piotrowski, Robert W. Vallin and Eric Wingler

Open Access

|Nov 2012

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.

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Articles in this issue

DOI: https://doi.org/10.2478/v10127-009-0004-y | Journal eISSN: 1338-9750 | Journal ISSN: 12103195

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Language: English

Page range: 39 - 49

Published on: Nov 12, 2012

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

separately open topology,

separate continuity.

Related subjects:

Mathematics,

General mathematics

© 2012 Zbigniew Piotrowski, Robert W. Vallin, Eric Wingler, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons License.

Volume 42 (2009): Issue 1 (April 2009)