Open AccessOn a Lindenbaum Composition Theorem
Author(s) -
Jaroslav Šupina,
Dávid Uhrik
Publication year - 2019
Publication title -
tatra mountains mathematical publications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.171
H-Index - 12
eISSN - 1338-9750
pISSN - 1210-3195
DOI - 10.2478/tmmp-2019-0025
Subject(s) - mathematics , topological space , characterization (materials science) , composition (language) , class (philosophy) , space (punctuation) , pure mathematics , property (philosophy) , topology (electrical circuits) , discrete mathematics , combinatorics , computer science , artificial intelligence , linguistics , philosophy , materials science , epistemology , nanotechnology , operating system
We discuss several questions about Borel measurable functions on a topological space. We show that two Lindenbaum composition theorems [Lindenbaum, A. Sur les superpositions des fonctions représentables analytiquement , Fund. Math. 23 (1934), 15–37] proved for the real line hold in perfectly normal topological space as well. As an application, we extend a characterization of a certain class of topological spaces with hereditary Jayne-Rogers property for perfectly normal topological space. Finally, we pose an interesting question about lower and upper Δ 0 2 -measurable functions.