<abstract xmlns="http://www.w3.org/1999/xhtml"><p> A real-valued function <italic>f </italic>on R is strongly countably continuous provided that there is a sequence of continuous functions (<italic>fn</italic>)<italic>n∈</italic>N such that the graph of <italic>f </italic>is contained in the union of the graphs of <italic>fn</italic>.</p><p>Some examples of interesting strongly countably continuous functions are given: one for which the inverse function is not strongly countably continuous, another which is an additive discontinuous function with a big image and a function which is approximately and <italic>I</italic>-approximately continuous, but it is not strongly countably continuous.</p></abstract>

A real-valued function f on R is strongly countably continuous provided that there is a sequence of continuous functions (fn)n∈N such that the graph of f is contained in the union of the graphs of fn.Some examples of interesting strongly countably continuous functions are given: one for which the inverse function is not strongly countably continuous, another which is an additive discontinuous function with a big image and a function which is approximately and I-approximately continuous, but it is not strongly countably continuous.

On strongly countably continuous functions

Department of Mathematics and Computer Science Łódź University Banacha 22 PL–90-238 Łódź POLAND

Tatra Mountains Mathematical Publications

{"article-title":"On strongly countably continuous functions"}

A real-valued function f on R is strongly countably continuous provided that there is a sequence of continuous functions (fn)n∈N such that the graph of f is...

On strongly countably continuous functions

Published Online: Nov 12, 2012

Page range: 81 - 86

DOI: https://doi.org/10.2478/v10127-009-0008-7

Keywords
countable decomposition, additive functions, approximate and I-approximate continuity, Baire∗1 functions.

This content is open access.

On strongly countably continuous functions

Published Online: Nov 12, 2012

Page range: 81 - 86

DOI: https://doi.org/10.2478/v10127-009-0008-7

Keywordscountable decomposition, additive functions, approximate and I-approximate continuity, Baire∗1 functions.

This content is open access.

Keywords
countable decomposition, additive functions, approximate and I-approximate continuity, Baire∗1 functions.