Complements of convex topologies on products of finite totally ordered spaces

Abdelwaheb Mhemdi; Tom Richmond

doi:10.1007/s11117-017-0472-2

Complements of convex topologies on products of finite totally ordered spaces

Abdelwaheb Mhemdi
, Tom Richmond

Mathematics

Western Kentucky University

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

2 Scopus citations

Abstract

Let X be a finite product of finite totally ordered topological spaces. We show that in the lattice of topologies on X, every convex topology τ on X has a convex complement τ^′.

Original language	English
Pages (from-to)	1369-1382
Number of pages	14
Journal	Positivity
Volume	21
Issue number	4
DOIs	https://doi.org/10.1007/s11117-017-0472-2
State	Published - 1 Dec 2017

Keywords

Complement
Convex topology
Ordered topological space

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10.1007/s11117-017-0472-2

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title = "Complements of convex topologies on products of finite totally ordered spaces",

abstract = "Let X be a finite product of finite totally ordered topological spaces. We show that in the lattice of topologies on X, every convex topology τ on X has a convex complement τ′.",

keywords = "Complement, Convex topology, Ordered topological space",

author = "Abdelwaheb Mhemdi and Tom Richmond",

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year = "2017",

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doi = "10.1007/s11117-017-0472-2",

language = "English",

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T1 - Complements of convex topologies on products of finite totally ordered spaces

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AU - Richmond, Tom

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N2 - Let X be a finite product of finite totally ordered topological spaces. We show that in the lattice of topologies on X, every convex topology τ on X has a convex complement τ′.

AB - Let X be a finite product of finite totally ordered topological spaces. We show that in the lattice of topologies on X, every convex topology τ on X has a convex complement τ′.

KW - Complement

KW - Convex topology

KW - Ordered topological space

UR - https://www.scopus.com/pages/publications/85010937732

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DO - 10.1007/s11117-017-0472-2

M3 - Article

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VL - 21

SP - 1369

EP - 1382

JO - Positivity

JF - Positivity

IS - 4

ER -

Complements of convex topologies on products of finite totally ordered spaces

Abstract

Keywords

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