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Start Over Subject Stone-Čech compactification

1. Flow compactifications of nondiscrete monoids, idempotents and Hindman’s theorem

Creator:
Ball, Richard N. and Hagler, James N.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
flow, Stone-Čech compactification, and Hindman’s theorem
Language:
English
Description:
We describe the extension of the multiplication on a not-necessarily-discrete topological monoid to its flow compactification. We offer two applications. The first is a nondiscrete version of Hindman’s Theorem, and the second is a characterization of the projective minimal and elementary flows in terms of idempotents of the flow compactification of the monoid.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. On van Douwen spaces and retracts of βN

Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
βN, retracts, two to one map, and Stone-Čech compactification
Language:
English
Description:
Eric van Douwen produced in 1993 a maximal crowded extremally disconnected regular space and showed that its Stone-Čech compactification is an at most two-to-one image of βN. We prove that there are non-homeomorphic such images. We also develop some related properties of spaces which are absolute retracts of βN expanding on earlier work of Balcar and Błaszczyk (1990) and Simon (1987).
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

3. When spectra of lattices of z-ideals are Stone-Čech compactifications

Creator:
Dube, Themba
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
completely regular frame, coherent frame, z-ideal, d-ideal, Stone-Čech compactification, and booleanization
Language:
English
Description:
Let X be a completely regular Hausdorff space and, as usual, let C(X) denote the ring of real-valued continuous functions on X. The lattice of z-ideals of C(X) has been shown by Martínez and Zenk (2005) to be a frame. We show that the spectrum of this lattice is (homeomorphic to) βX precisely when X is a P-space. This we actually show to be true not only in spaces, but in locales as well. Recall that an ideal of a commutative ring is called a d-ideal if whenever two elements have the same annihilator and one of the elements belongs to the ideal, then so does the other. We characterize when the spectrum of the lattice of d-ideals of C(X) is the Stone-Čech compactification of the largest dense sublocale of the locale determined by X. It is precisely when the closure of every open set of X is the closure of some cozero-set of X.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public