A Separately Continuous Function Not Somewhat Continuous

Wojciech Bielas

doi:10.2478/amsil-2021-0013

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A Separately Continuous Function Not Somewhat Continuous

Annales Mathematicae Silesianae

Volume 36 (2022): Issue 1 (March 2022)

By: Wojciech Bielas

Open Access

|Oct 2021

Abstract

We construct a separately continuous function f : ℚ × ℚ → [0; 1] and a dense subset D ⊆ ℚ × ℚ such that f[D] is not dense in f[ℚ × ℚ], in other words, f is separately continuous and not somewhat (feebly) continuous.

References

[1] Z. Frolík, Remarks concerning the invariance of Baire spaces under mappings, Czechoslovak Math. J. 11(86) (1961), no. 3, 381–385.
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[2] K.R. Gentry, H.B. Hoyle III, Somewhat continuous functions, Czechoslovak Math. J. 21(96) (1971), no. 1, 5–12.
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[3] N.F.G. Martin, Quasi-continuous functions on product spaces, Duke Math. J. 28 (1961), no. 1, 39–43.
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[4] T. Neubrunn, Generalized continuity and separate continuity, Math. Slovaca 27 (1977), no. 3, 307–314.
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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2021-0013 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 26 - 29

Submitted on: Jul 8, 2021

Accepted on: Sep 26, 2021

Published on: Oct 11, 2021

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

separate continuity,

somewhat continuous function

Related subjects:

Mathematics,

General mathematics

© 2021 Wojciech Bielas, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Volume 36 (2022): Issue 1 (March 2022)