Limits of sequences of Darboux-like mappings |
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Author |
Maslenizza.ua@gmail.com
Yuriy Fedkovych Chernivtsi National University
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Abstract |
We call a mapping $f\colon X\to Y$ an $l$-Darboux mapping if the image of any arcwise connected subset of $X$ is connected.
We prove that the class of $l$-Darboux $F_\sigma$-measurable mappings of a topological space to a metric space is closed with respect to uniform limits.
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Keywords |
uniform limit; Darboux function; $F_\sigma$-measurable function; weakly Gibson function
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Reference |
1. A. Bruckner, Differentiation of real functions, 2nd ed., Providence, RI: American Mathematical Society,
1994, 195 p.
2. R. Gibson, T. Natkaniec, Darboux-like functions, Real Anal. Exchange, 22 (1996-97), ¹2, 492–533. 3. O. Karlova, V. Mykhaylyuk, On Gibson functions with connected graphs, Math. Slovaca, 63 (2013), ¹3. 4. K. Kellum, Functions that separate $X\times\mathbb R$, Houston J. Math., 36 (2010), 1221–1226. 5. K. Kuratowski, Topology, V.1, M.: Mir, 1966. (in Russian) 6. A. Lindenbaum, Sur quelques proprieties des fonctions de variable reelle, Ann. Soc. Math. Polon., 6 (1927), 129–130. 7. H. Pawlak, R.J. Pawlak, On weakly Darboux functions and some problem connected with the Morrey monotonicity, Journal of Applied Analysis, 1 (1995), ¹2, 135–144. |
Pages |
132-136
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Volume |
40
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Issue |
2
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Year |
2013
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Journal |
Matematychni Studii
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