On the sobriety of the inverse topology

Papiya Bhattacharjee; Themba Dube

doi:10.1007/s00012-016-0414-z

On the sobriety of the inverse topology

Papiya Bhattacharjee
, Themba Dube

School of Science (Behrend)

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

2 Scopus citations

Abstract

An algebraic frame L with the finite intersection property (FIP) on compact elements is said to be polarised if every minimal prime element in it is complemented. In this note, we give a necessary and sufficient condition for the inverse topology on the set of minimal prime elements of such a frame to be sober. We also establish some sufficient conditions for sobriety when the polarisation condition is relaxed.

Original language	English (US)
Pages (from-to)	445-454
Number of pages	10
Journal	Algebra Universalis
Volume	76
Issue number	4
DOIs	https://doi.org/10.1007/s00012-016-0414-z
State	Published - Dec 1 2016

All Science Journal Classification (ASJC) codes

Logic
Algebra and Number Theory

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10.1007/s00012-016-0414-z

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abstract = "An algebraic frame L with the finite intersection property (FIP) on compact elements is said to be polarised if every minimal prime element in it is complemented. In this note, we give a necessary and sufficient condition for the inverse topology on the set of minimal prime elements of such a frame to be sober. We also establish some sufficient conditions for sobriety when the polarisation condition is relaxed.",

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AU - Dube, Themba

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N2 - An algebraic frame L with the finite intersection property (FIP) on compact elements is said to be polarised if every minimal prime element in it is complemented. In this note, we give a necessary and sufficient condition for the inverse topology on the set of minimal prime elements of such a frame to be sober. We also establish some sufficient conditions for sobriety when the polarisation condition is relaxed.

AB - An algebraic frame L with the finite intersection property (FIP) on compact elements is said to be polarised if every minimal prime element in it is complemented. In this note, we give a necessary and sufficient condition for the inverse topology on the set of minimal prime elements of such a frame to be sober. We also establish some sufficient conditions for sobriety when the polarisation condition is relaxed.

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On the sobriety of the inverse topology

Abstract

All Science Journal Classification (ASJC) codes

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