<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We study the joint continuity of mappings of two variables. In particular, we show that for a Baire space X, a second countable space Y and a metric space Z, a map f : X × Y → Z has the Hahn property (i.e., there is a residual subset A of X such that A × Y ⊆ C(f)) if and only if f is locally equi-cliquish with respect to y and {x ∈ X: f<sup>x</sup> is continuous} is a residual subset of X.</p></abstract>

We study the joint continuity of mappings of two variables. In particular, we show that for a Baire space X, a second countable space Y and a metric space Z, a map f : X × Y → Z has the Hahn property (i.e., there is a residual subset A of X such that A × Y ⊆ C(f)) if and only if f is locally equi-cliquish with respect to y and {x ∈ X: fx is continuous} is a residual subset of X.

Equi-Cliquishness and The Hahn Property

Chernivtsi National University Department of Mathematical Kotsubinsky Str. 2 58012 Chernivtsi UKRAINE

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"Equi-Cliquishness and The Hahn Property"}

We study the joint continuity of mappings of two variables. In particular, we show that for a Baire space X, a second countable space Y and a metric space Z, a...

Equi-Cliquishness and The Hahn Property

Published Online: Aug 04, 2016

Page range: 85 - 92

Received: Apr 30, 2015

DOI: https://doi.org/10.1515/tmmp-2016-0007

Keywords
equi-cliquishness, locally equi-cliquishness, cliquishness, joint continuity, Hahn property

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Equi-Cliquishness and The Hahn Property

Published Online: Aug 04, 2016

Page range: 85 - 92

Received: Apr 30, 2015

DOI: https://doi.org/10.1515/tmmp-2016-0007

Keywordsequi-cliquishness, locally equi-cliquishness, cliquishness, joint continuity, Hahn property

© 2016

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
equi-cliquishness, locally equi-cliquishness, cliquishness, joint continuity, Hahn property