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Notes on direct limits of complete lattices and frames

✍ Scribed by Sheng Ye; Hui Kou

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 81 KB
Volume: 171
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(01)00147-5

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✦ Synopsis

In traditional topology, it is known that an inverse limit of continua (compact Hausdor connected spaces) is a continuum. This paper gives corresponding results in locales: we show that a direct limit of compact normal (or, of compact normal connected) frames is normal (resp. normal connected). Some of the preparatory results hold in broader categories, and in fact we will give su cient conditions for an inverse limit of complete lattices to be compact (or compact connected).

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