Median pretrees and functions of bounded variation

Michael Megrelishvili

doi:https://doi.org/10.1016/j.topol.2020.107383

Median pretrees and functions of bounded variation

Michael Megrelishvili

Department of Mathematics

Bar-Ilan University

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

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

Keywords

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

All Science Journal Classification (ASJC) codes

Geometry and Topology

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https://doi.org/10.1016/j.topol.2020.107383

Cite this

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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.",

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AB - 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.

KW - Baire class 1

KW - Bounded variation

KW - Dendrite

KW - Dendrone

KW - Fragmented function

KW - Helly's selection theorem

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KW - Pretree

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M3 - مقالة

SN - 0166-8641

VL - 285

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 107383

ER -

Median pretrees and functions of bounded variation

Abstract

Keywords

All Science Journal Classification (ASJC) codes

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