<abstract xmlns="http://www.w3.org/1999/xhtml"><p> We study separate and joint properties of pointwise discontinuity, simple continuity and mild continuity of functions of two variables. In particular, it is shown that for a Baire space X, aBaire space Y which has a countable pseudobase and for a metric space Z, a function ƒ : X×Y → Z is pointwise discontinuous if and only if f satisfies (α, β)-condition and condition (C), and M = {x ∊ X : C(ƒ<sup>x</sup>) = Y } is a residual subset of X. In addition, a characterization of simple continuity for mappings of one and two variables is given</p></abstract>

We study separate and joint properties of pointwise discontinuity, simple continuity and mild continuity of functions of two variables. In particular, it is shown that for a Baire space X, aBaire space Y which has a countable pseudobase and for a metric space Z, a function ƒ : X×Y → Z is pointwise discontinuous if and only if f satisfies (α, β)-condition and condition (C), and M = {x ∊ X : C(ƒx) = Y } is a residual subset of X. In addition, a characterization of simple continuity for mappings of one and two variables is given

Separate and Joint Properties of some Analogues of Pointwise Discontinuity

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

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"Separate and Joint Properties of some Analogues of Pointwise Discontinuity"}

We study separate and joint properties of pointwise discontinuity, simple continuity and mild continuity of functions of two variables. In particular, it is...

Separate and Joint Properties of some Analogues of Pointwise Discontinuity

Published Online: Aug 15, 2014

Page range: 155 - 167

Received: Feb 05, 2014

DOI: https://doi.org/10.2478/tmmp-2014-0014

Keywords
simple continuity, mild continuity, cliquishness, pointwise discontinuity

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Separate and Joint Properties of some Analogues of Pointwise Discontinuity

Published Online: Aug 15, 2014

Page range: 155 - 167

Received: Feb 05, 2014

DOI: https://doi.org/10.2478/tmmp-2014-0014

Keywordssimple continuity, mild continuity, cliquishness, pointwise discontinuity

© 2014

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
simple continuity, mild continuity, cliquishness, pointwise discontinuity