Ends of non-metrizable manifolds: A generalized bagpipe theorem

David Fernández-Bretón; Nicholas G. Vlamis

doi:10.1016/j.topol.2022.108017

Ends of non-metrizable manifolds: A generalized bagpipe theorem

David Fernández-Bretón, Nicholas G. Vlamis

Escuela Superior de Física y Matemáticas (ESFM)

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

Abstract

We initiate the study of ends of non-metrizable manifolds and introduce the notion of short and long ends. Using the theory developed, we provide a characterization of (non-metrizable) surfaces that can be written as the topological sum of a metrizable manifold plus a countable number of “long pipes” in terms of their spaces of ends; this is a direct generalization of Nyikos's bagpipe theorem.

Translated title of the contribution	Extremos de variedades no metrizables: un teorema de gaita generalizado
Original language	English
Article number	108017
Journal	Topology and its Applications
Volume	310
DOIs	https://doi.org/10.1016/j.topol.2022.108017
State	Published - 1 Apr 2022

Keywords

Bagpipe
Freudenthal compactification
Non-metrizable manifolds
Nyikos's bagpipe theorem
Space of ends

Access to Document

10.1016/j.topol.2022.108017

Cite this

@article{2f5ef7035f0d45478ed9d2d6cd7354ff,

title = "Ends of non-metrizable manifolds: A generalized bagpipe theorem",

abstract = "We initiate the study of ends of non-metrizable manifolds and introduce the notion of short and long ends. Using the theory developed, we provide a characterization of (non-metrizable) surfaces that can be written as the topological sum of a metrizable manifold plus a countable number of “long pipes” in terms of their spaces of ends; this is a direct generalization of Nyikos's bagpipe theorem.",

keywords = "Bagpipe, Freudenthal compactification, Non-metrizable manifolds, Nyikos's bagpipe theorem, Space of ends",

author = "David Fern{\'a}ndez-Bret{\'o}n and Vlamis, {Nicholas G.}",

note = "Publisher Copyright: {\textcopyright} 2022 Elsevier B.V.",

year = "2022",

month = apr,

day = "1",

doi = "10.1016/j.topol.2022.108017",

language = "Ingl{\'e}s",

volume = "310",

journal = "Topology and its Applications",

issn = "0166-8641",

publisher = "Elsevier",

}

TY - JOUR

T1 - Ends of non-metrizable manifolds

T2 - A generalized bagpipe theorem

AU - Fernández-Bretón, David

AU - Vlamis, Nicholas G.

PY - 2022/4/1

Y1 - 2022/4/1

N2 - We initiate the study of ends of non-metrizable manifolds and introduce the notion of short and long ends. Using the theory developed, we provide a characterization of (non-metrizable) surfaces that can be written as the topological sum of a metrizable manifold plus a countable number of “long pipes” in terms of their spaces of ends; this is a direct generalization of Nyikos's bagpipe theorem.

AB - We initiate the study of ends of non-metrizable manifolds and introduce the notion of short and long ends. Using the theory developed, we provide a characterization of (non-metrizable) surfaces that can be written as the topological sum of a metrizable manifold plus a countable number of “long pipes” in terms of their spaces of ends; this is a direct generalization of Nyikos's bagpipe theorem.

KW - Bagpipe

KW - Freudenthal compactification

KW - Non-metrizable manifolds

KW - Nyikos's bagpipe theorem

KW - Space of ends

UR - http://www.scopus.com/inward/record.url?scp=85123695755&partnerID=8YFLogxK

U2 - 10.1016/j.topol.2022.108017

DO - 10.1016/j.topol.2022.108017

M3 - Artículo

AN - SCOPUS:85123695755

SN - 0166-8641

VL - 310

JO - Topology and its Applications

JF - Topology and its Applications

M1 - 108017

ER -

Ends of non-metrizable manifolds: A generalized bagpipe theorem

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this