Median pretrees and functions of bounded variation

Michael Megrelishvili

doi:10.1016/j.topol.2020.107383

Median pretrees and functions of bounded variation

Michael Megrelishvili

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

We introduce functions of bounded variation on median algebras and study some properties for median pretrees. We show that if X is a compact median pretree (e.g., a dendron) in its shadow topology then every function f:X→R of bounded variation has the point of continuity property (Baire 1, if X, in addition, is metrizable). We prove a generalized version of Helly's selection theorem for a sequence of functions with total bounded variation defined on a Polish median pretree X.

Original language	English
Article number	107383
Journal	Topology and its Applications
Volume	285
DOIs	https://doi.org/10.1016/j.topol.2020.107383
State	Published - 1 Nov 2020

Bibliographical note

Publisher Copyright:
© 2020

Funding

This research was supported by a grant of the Israel Science Foundation ( ISF 1194/19 ).

Funders	Funder number
Israel Science Foundation	ISF 1194/19

Keywords

Baire class 1
Bounded variation
Dendrite
Dendrone
Fragmented function
Helly's selection theorem
Median algebra
Pretree

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10.1016/j.topol.2020.107383

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KW - Dendrone

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Median pretrees and functions of bounded variation

Abstract

Bibliographical note

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Keywords

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