<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

Publié en ligne: 15 août 2014

Pages: 155 - 167

Reçu: 05 févr. 2014

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

Mots clés
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

Publié en ligne: 15 août 2014

Pages: 155 - 167

Reçu: 05 févr. 2014

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

Mots cléssimple continuity, mild continuity, cliquishness, pointwise discontinuity

© 2014

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

Mots clés
simple continuity, mild continuity, cliquishness, pointwise discontinuity