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The Stone–Čech compactification of locales, III

✍ Scribed by Bernhard Banaschewski; Christopher J. Mulvey

Publisher
Elsevier Science
Year
2003
Tongue
English
Weight
134 KB
Volume
185
Category
Article
ISSN
0022-4049

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✦ Synopsis

The Stone-Ä Cech compactiÿcation of a locale L is shown to be obtained constructively by taking the Lindenbaum locale of the theory of almost prime completely regular ÿlters on L. Modifying the theory by replacing the completely below relation by the strongly below relation yields instead the compact regular re ection, with corresponding results for the compact zerodimensional re ection, indeed for any compactiÿcation of a locale.

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✍ James Keesling; R.B. Sher 📂 Article 📅 1978 🏛 Elsevier Science ⚖ 947 KB

In thiqpaper it is shown that if X is a connected space which is not pesuJocompact, then @X is not mov#ble and does not have metric shape. In particular /3X cannot hzde trivial shape. It is also shown tdar if X is Linda liif and K c /3X --' X is a continuum, then K cannot be movable or have metric s