Samuel compactification and uniform coreflection of nearness σ-frames

2006 ◽  
Vol 56 (4) ◽  
pp. 1229-1241 ◽  
Author(s):  
Inderasan Naidoo
Keyword(s):  
Samuel Compactification

scholarly journals On the order scale of a uniform space

1983 ◽  
Vol 34 (2) ◽  
pp. 248-257 ◽  
Author(s):  
D. C. Kent
Keyword(s):  
Boolean Algebra ◽  
Distributive Lattice ◽  
Closed Subspace ◽  
Uniform Space ◽  
Order Topology ◽  
Totally Bounded ◽  
Samuel Compactification ◽  
Closed Image ◽  
Atomic Boolean Algebra

AbstractThe order topology is compact and T2 in both the scale and retracted scale of any uniform space (S, U). if (S, U) is T2 and totally bounded, the Samuel compactification associated with (S, U) can be obtained by uniformly embedding (S, U) in its order retracted scale (that is, the retracted scale with its order topology). This implies that every compact T2 space is both a closed subspace of a complete, infinitely distributive lattice in its order topology, and also a continuous, closed image of a closed subspace of a complete atomic Boolean algebra in its order topology.

Samuel compactification and completion of uniform frames

1990 ◽  
Vol 108 (1) ◽  
pp. 63-78 ◽  
Author(s):  
B. Banaschewski ◽  
A. Pultr
Keyword(s):  
Uniform Space ◽  
The Other ◽  
Uniform Spaces ◽  
Samuel Compactification ◽  
Uniform Frame ◽  
The One ◽  
Uniform Frames

The aim of this paper is twofold: first, to construct the compact regular coreflection of uniform frames, that is, the frame counterpart of the Samuel compactification of uniform spaces (Samuel [10]), and then to use this for a new description of the completion of a uniform frame, as an alternative to those previously given by Isbell [6] on the one hand and Kříž [8] on the other. In addition, we present a few further results, as well as new proofs of known ones, that are naturally connected with completions and arise particularly easily from our approach to them. Most prominently among these, we identify the uniform space of minimal Cauchy filters of a uniform frame as the spectrum of its completion.

scholarly journals Extremal structure and Samuel compactification

2009 ◽  
Vol 156 (18) ◽  
pp. 3109-3113
Author(s):  
J.C. Navarro-Pascual
Keyword(s):  
Samuel Compactification ◽  
Extremal Structure

Compactifications of partial frames via strongly regular ideals

2018 ◽  
Vol 68 (2) ◽  
pp. 285-298 ◽  
Author(s):  
John Frith ◽  
Anneliese Schauerte
Keyword(s):  
Completely Regular ◽  
Partial Frame ◽  
Samuel Compactification ◽  
Small Collection ◽  
Strongly Regular ◽  
Similarities And Differences

Abstract Partial frames provide a fertile context in which to do pointfree structured and unstructured topology, using a small collection of axioms of an elementary nature. Amongst other things they can be used to investigate similarities and differences between frames, σ-frames and κ-frames. In this paper, the theory of strong inclusions for partial frames is used to describe compactifications of completely regular partial frames; the elements of these compactifications are given explicitly as strongly regular ideals. This is independent of and encompasses the theory of compactifications for frames. As an application, we revisit the Samuel compactification of a uniform partial frame.

On completion in the category SSNσFrm

2013 ◽  
Vol 63 (2) ◽  
Author(s):  
Inderasan Naidoo
Keyword(s):  
Similar Construction ◽  
Total Boundedness ◽  
Czechoslovak Math ◽  
Samuel Compactification ◽  
Phd Thesis ◽  
Uniform Frames

AbstractWe introduce the category SSN σ Frm of super strong nearness σ-frames and show the existence of a completion for a super strong nearness σ-frame unique up to isomorphism by the similar construction presented in [WALTERS-WAYLAND, J. L.: Completeness and Nearly Fine Uniform Frames. PhD Thesis, Univ. Catholique de Louvain, 1996] and [WALTERS-WAYLAND, J. L.: A Shirota Theorem for frames, Appl. Categ. Structures 7 (1999), 271–277]. Completion is also shown to be a coreflection in SSN σ Frm. We also engage with the notion of total boundedness for nearness σ-frames and provide a characterization of the Samuel compactification of a nearness σ-frame alternative to the description in [NAIDOO, I.: Samuel compactification and uniform coreflection of nearness σ-frames, Czechoslovak Math. J. 56(131) (2006), 1229–1241].

scholarly journals Universal Minimal Flows of Groups of Automorphisms of Uncountable Structures

2013 ◽  
Vol 56 (4) ◽  
pp. 709-722
Author(s):  
Dana Bartošová
Keyword(s):  
Topological Group ◽  
Ramsey Theory ◽  
Original Description ◽  
Simple Computation ◽  
Minimal Flow ◽  
Samuel Compactification ◽  
Groups Of Automorphisms ◽  
The Right

Abstract.It is a well-known fact that the greatest ambit for a topological group G is the Samuel compactification of G with respect to the right uniformity on G. We apply the original description by Samuel from 1948 to give a simple computation of the universal minimal flow for groups of automorphisms of uncountable structures using Fraϊssé theory and Ramsey theory. This work generalizes some of the known results about countable structures

scholarly journals The Samuel compactification for quasi-uniform biframes

2009 ◽  
Vol 156 (12) ◽  
pp. 2116-2122 ◽  
Author(s):  
John Frith ◽  
Anneliese Schauerte
Keyword(s):  
Samuel Compactification
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