<abstract xmlns="http://www.w3.org/1999/xhtml">We discuss several questions about Borel measurable functions on a topological space. We show that two Lindenbaum composition theorems [Lindenbaum, A. <italic>Sur les superpositions des fonctions représentables analytiquement</italic>, Fund. Math. <bold>23</bold> (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 Δ02-measurable functions.</abstract>

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 Δ02-measurable functions.

On a Lindenbaum Composition Theorem

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On a Lindenbaum Composition Theorem"}

We discuss several questions about Borel measurable functions on a topological space. We show that two Lindenbaum composition theorems [Lindenbaum, A. Sur les...

On a Lindenbaum Composition Theorem

Published Online: Nov 15, 2019

Page range: 145 - 158

Received: Nov 30, 2018

DOI: https://doi.org/10.2478/tmmp-2019-0025

Keywords
semicontinuous function, Young hierarchy, Δ-measurable function, composition, piecewise continuous

© 2019 Jaroslav Šupina et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On a Lindenbaum Composition Theorem

Published Online: Nov 15, 2019

Page range: 145 - 158

Received: Nov 30, 2018

DOI: https://doi.org/10.2478/tmmp-2019-0025

Keywordssemicontinuous function, Young hierarchy, Δ-measurable function, composition, piecewise continuous

© 2019 Jaroslav Šupina et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
semicontinuous function, Young hierarchy, Δ-measurable function, composition, piecewise continuous