Limits of sequences of feebly-type continuous functions
Abstract
We consider the following families of real-valued functions defined on ℝ2: 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.
Keywords
functions in two variables; feebly continuity; very feebly continuity; two-feebly continuity; pointwise limit; topology of uniform convergence
References
2. Á. Császár and M. Laczkovich, Discrete and equal convergence, Studia Sci. Math. Hungar. 10 (1975), no. 3, 463–472 (1978).
3. I. Leader, A note on feebly continuous functions, Topology Appl. 156 (2009), no. 16, 2629–2631.
Instytut Matematyki, Politechnika Łódzka Poland
https://orcid.org/0000-0003-3808-7706
Instytut Matematyki, Wydział Matekatyki, Fizyki i Informatyki, Uniwersytet Gdański Poland
Centrum Nauczania Matematyki i Fizyki oraz Instytut Matematyki, Politechnika Łódzka Poland
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