Separate and Joint Properties of some Analogues of Pointwise Discontinuity

Vasyl’ Nesterenko

doi:10.2478/tmmp-2014-0014

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Separate and Joint Properties of some Analogues of Pointwise Discontinuity

Tatra Mountains Mathematical Publications

Volume 58 (2014): Issue 1 (March 2014)

By: Vasyl’ Nesterenko

Open Access

|Aug 2014

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(ƒ^x) = Y } is a residual subset of X. In addition, a characterization of simple continuity for mappings of one and two variables is given

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Articles in this issue

DOI: https://doi.org/10.2478/tmmp-2014-0014 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 155 - 167

Submitted on: Feb 5, 2014

Published on: Aug 15, 2014

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

simple continuity,

mild continuity,

cliquishness,

pointwise discontinuity

Related subjects:

Mathematics,

General mathematics

© 2014 Vasyl’ Nesterenko, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 58 (2014): Issue 1 (March 2014)