A characterization of the uniform convergence points set of some convergent sequence of functions
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Olena Karlova
Abstract
We characterize the uniform convergence points set of a pointwisely convergent sequence of real-valued functions defined on a perfectly normal space. We prove that if X is a perfectly normal space which can be covered by a disjoint sequence of dense subsets and A ⊆ X, then A is the set of points of the uniform convergence for some convergent sequence (fn)n∈ω of functions fn : X → ℝ if and only if A is Gδ-set which contains all isolated points of X. This result generalizes a theorem of Ján Borsík published in 2019.
Acknowledgement
I am very grateful to the reviewers for their careful reading of the manuscript and valuable remarks which allowed to improve the paper.
Dedicated to the memory of Ján Borsík
(Communicated by Tomasz Natkaniec )
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© 2021 Mathematical Institute Slovak Academy of Sciences
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Articles in the same Issue
- Regular papers
- Prof. RNDr. Michal Fečkan, DrSc. – Sexagenarian?
- Tribonacci numbers with two blocks of repdigits
- Padovan numbers that are concatenations of two distinct repdigits
- On the 2-rank and 4-rank of the class group of some real pure quartic number fields
- A general inverse matrix series relation and associated polynomials – II
- Some hardy type inequalities with finsler norms
- Starlikeness and convexity of the product of certain multivalent functions with higher-order derivatives
- Block Hessenberg matrices and spectral transformations for matrix orthogonal polynomials on the unit circle
- How is the period of a simple pendulum growing with increasing amplitude?
- Fourier transforms of convolution operators on orlicz spaces
- Some characterizations of property of trans-Sasakian 3-manifolds
- P-Adic metric preserving functions and their analogues
- On statistical convergence of sequences of closed sets in metric spaces
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- Donsker’s fuzzy invariance principle under the Lindeberg condition
- Characterization of generalized Gamma-Lindley distribution using truncated moments of order statistics
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