Hewitt's irresolvability and induced Sublocales in spatial frames

被引：4

作者：

Baboolal, Dharmanand ^{[1
]}

Picado, Jorge ^{[2
]}

Pillay, Paranjothi ^{[1
]}

Pultr, Ales ^{[3
,4
]}

机构：

[1] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, ZA-4000 Durban, South Africa

[2] Univ Coimbra, CMUC, Dept Math, P-3001501 Coimbra, Portugal

[3] Charles Univ Prague, Dept Appl Math, Malostranske Nam 24, CR-11800 Prague 1, Czech Republic

[4] Charles Univ Prague, CE ITI, MFF, Malostranske Nam 24, CR-11800 Prague 1, Czech Republic

来源：

QUAESTIONES MATHEMATICAE | 2020年 / 43卷 / 11期

关键词：

Frame; spatial frame; locale; sublocale; sublocale lattice; induced sublocale; T-D; -axiom; scattered space; hereditarily irresolvable space;

D O I：

10.2989/16073606.2019.1646832

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Sublocales of frames, even those representing subspaces (induced sublo-cales), are typically not complemented in the lattice of all sublocales. We present a necessary and sucient condition for an induced sublocale to be so, and prove that all induced sublocales are complemented iff the space in question is hereditarily irresolvable, a property slightly weaker than - and in a broad class of spaces equivalent with - scatteredness (under which condition, by Simmons' result all sublocales are complemented).

引用

页码：1601 / 1612

页数：12

共 12 条

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