Limits of Sequences of Feebly-Type Continuous Functions

Balcerzak, Marek; Natkaniec, Tomasz; Terepeta, Małgorzata

doi:10.2478/amsil-2020-0011

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Limits of Sequences of Feebly-Type Continuous Functions

Annales Mathematicae Silesianae

Volume 34 (2020): Issue 1 (July 2020)

By: Marek Balcerzak, Tomasz Natkaniec and Małgorzata Terepeta

Open Access

|Jul 2020

Abstract

We consider the following families of real-valued functions defined on 𝕉²: feebly continuous functions (FC), very feebly continuous functions (VFC), and two-feebly continuous functions (TFC). It is known that the inclusions FC ⊂ VFC ⊂ TFC are proper. We study pointwise and uniform limits of sequences with terms taken from these families.

References

[1] M. Balcerzak, T. Natkaniec, and M. Terepeta, Families of feebly continuous functions and their properties, Topology Appl. 272 (2020), 107077, 12 pp.10.1016/j.topol.2020.107077
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[2] Á. Császár and M. Laczkovich, Discrete and equal convergence, Studia Sci. Math. Hungar. 10 (1975), no. 3, 463–472 (1978).
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[3] I. Leader, A note on feebly continuous functions, Topology Appl. 156 (2009), no. 16, 2629–2631.10.1016/j.topol.2009.04.009
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DOI: https://doi.org/10.2478/amsil-2020-0011 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 27 - 35

Submitted on: Oct 14, 2019

Accepted on: Jun 3, 2020

Published on: Jul 9, 2020

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

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

functions in two variables,

feebly continuity,

very feebly continuity,

two-feebly continuity,

pointwise limit,

topology of uniform convergence

Related subjects:

Mathematics,

General mathematics

© 2020 Marek Balcerzak, Tomasz Natkaniec, Małgorzata Terepeta, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

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