Partitions of unity and coverings

Kyle Austin; Jerzy Dydak

doi:10.1016/j.topol.2014.05.015

Partitions of unity and coverings

Kyle Austin, Jerzy Dydak

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

2 Scopus citations

Abstract

The aim of this paper is to prove all well-known metrization theorems using partitions of unity. To accomplish this, we first discuss sufficient and necessary conditions for existence of U-small partitions of unity (partitions of unity subordinated to an open cover U of a topological space X).

Original language	English
Pages (from-to)	74-82
Number of pages	9
Journal	Topology and its Applications
Volume	173
DOIs	https://doi.org/10.1016/j.topol.2014.05.015
State	Published - 15 Aug 2014
Externally published	Yes

Keywords

Coverings
Metrization theorems
Partitions of unity

ASJC Scopus subject areas

Geometry and Topology

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10.1016/j.topol.2014.05.015

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title = "Partitions of unity and coverings",

abstract = "The aim of this paper is to prove all well-known metrization theorems using partitions of unity. To accomplish this, we first discuss sufficient and necessary conditions for existence of U-small partitions of unity (partitions of unity subordinated to an open cover U of a topological space X).",

keywords = "Coverings, Metrization theorems, Partitions of unity",

author = "Kyle Austin and Jerzy Dydak",

year = "2014",

month = aug,

day = "15",

doi = "10.1016/j.topol.2014.05.015",

language = "English",

volume = "173",

pages = "74--82",

journal = "Topology and its Applications",

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T1 - Partitions of unity and coverings

AU - Austin, Kyle

AU - Dydak, Jerzy

PY - 2014/8/15

Y1 - 2014/8/15

N2 - The aim of this paper is to prove all well-known metrization theorems using partitions of unity. To accomplish this, we first discuss sufficient and necessary conditions for existence of U-small partitions of unity (partitions of unity subordinated to an open cover U of a topological space X).

AB - The aim of this paper is to prove all well-known metrization theorems using partitions of unity. To accomplish this, we first discuss sufficient and necessary conditions for existence of U-small partitions of unity (partitions of unity subordinated to an open cover U of a topological space X).

KW - Coverings

KW - Metrization theorems

KW - Partitions of unity

UR - http://www.scopus.com/inward/record.url?scp=84901374782&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2014.05.015

DO - 10.1016/j.topol.2014.05.015

M3 - Article

AN - SCOPUS:84901374782

SN - 0166-8641

VL - 173

SP - 74

EP - 82

JO - Topology and its Applications

JF - Topology and its Applications

ER -

Partitions of unity and coverings

Abstract

Keywords

ASJC Scopus subject areas

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