<abstract xmlns="http://www.w3.org/1999/xhtml">

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

A Separately Continuous Function Not Somewhat Continuous

Annales Mathematicae Silesianae

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

{"article-title":"A Separately Continuous Function Not Somewhat Continuous"}

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...

A Separately Continuous Function Not Somewhat Continuous

Published Online: Oct 11, 2021

Page range: 26 - 29

Received: Jul 08, 2021

Accepted: Sep 26, 2021

DOI: https://doi.org/10.2478/amsil-2021-0013

Keywords
separate continuity, somewhat continuous function

© 2021 Wojciech Bielas, published by Sciendo

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

A Separately Continuous Function Not Somewhat Continuous

Published Online: Oct 11, 2021

Page range: 26 - 29

Received: Jul 08, 2021

Accepted: Sep 26, 2021

DOI: https://doi.org/10.2478/amsil-2021-0013

Keywordsseparate continuity, somewhat continuous function

© 2021 Wojciech Bielas, published by Sciendo

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

Keywords
separate continuity, somewhat continuous function