Short Proof of an Internal Characterization of Complete Regularity

1984 ◽  
Vol 27 (4) ◽  
pp. 461-462 ◽  
Author(s):  
Harald Brandenburg ◽  
Adam Mysior
Keyword(s):  
Short Proof ◽  
Complete Regularity ◽  
Completely Regular

AbstractA short proof is given of an internal characterization of completely regular spaces due to J. Kerstan.

An internal characterization of complete regularity

2020 ◽  
Vol 70 (3) ◽  
pp. 775-777
Author(s):  
Judyta Bąk ◽  
Andrzej Kucharski
Keyword(s):  
Short Proof ◽  
Complete Regularity

AbstractThis note presents a short proof of an internal characterization of complete regularity.

A Hahn-Banach Theorem in Subbase Convexity Theory

1980 ◽  
Vol 32 (4) ◽  
pp. 804-820 ◽  
Author(s):  
M. van de Vel
Keyword(s):  
Main Tool ◽  
Complete Regularity ◽  
Completely Regular ◽  
Banach Theorem ◽  
Convexity Theory ◽  
Hausdorff Compactifications

In the last fifteen years, topology has shown up with an increasing interest in the use of closed subbases. Starting from Frink's internal characterization of complete regularity (Frink [6]), DeGroot and Aarts used closed subbases to obtain Hausdorff compactifications of completely regular spaces, thus giving a characterization of the latter in terms of their subbases [1]. The main tool of that paper is the notion of a linked system, which naturally leads to the notions of supercompactness and superextensions [7]. After 1970, these two topics developed to indepedennt theories, with several deep results available at this moment. Most results up to 1976 are summarized in [12].

scholarly journals Complete regularity of Ellis semigroups of -actions

2020 ◽  
pp. 1-17
Author(s):  
MARCY BARGE ◽  
JOHANNES KELLENDONK
Keyword(s):  
Complete Regularity ◽  
Completely Regular ◽  
Ellis Semigroup ◽  
Totally Disconnected

Abstract It is shown that the Ellis semigroup of a $\mathbb Z$ -action on a compact totally disconnected space is completely regular if and only if forward proximality coincides with forward asymptoticity and backward proximality coincides with backward asymptoticity. Furthermore, the Ellis semigroup of a $\mathbb Z$ - or $\mathbb R$ -action for which forward proximality and backward proximality are transitive relations is shown to have at most two left minimal ideals. Finally, the notion of near simplicity of the Ellis semigroup is introduced and related to the above.

The coincidence approach to stochastic point processes

1975 ◽  
Vol 7 (1) ◽  
pp. 83-122 ◽  
Author(s):  
Odile Macchi
Keyword(s):  
Poisson Process ◽  
Probability Space ◽  
Point Processes ◽  
Counting Process ◽  
Regular Point ◽  
General Point ◽  
Completely Regular ◽  
Photon Process ◽  
Stochastic Point Processes

The structure of the probability space associated with a general point process, when regarded as a counting process, is reviewed using the coincidence formalism. The rest of the paper is devoted to the class of regular point processes for which all coincidence probabilities admit densities. It is shown that their distribution is completely specified by the system of coincidence densities. The specification formalism is stressed for ‘completely’ regular point processes. A construction theorem gives a characterization of the system of coincidence densities of such a process. It permits the study of most models of point processes. New results on the photon process, a particular type of conditioned Poisson process, are derived. New examples are exhibited, including the Gauss-Poisson process and the ‘fermion’ process that is suitable whenever the points are repulsive.

A Characterization of Universal Loeb Measurability for Completely Regular Hausdorff Spaces

1992 ◽  
Vol 44 (4) ◽  
pp. 673-690 ◽  
Author(s):  
J. M. Aldaz
Keyword(s):  
Hausdorff Spaces ◽  
Completely Regular ◽  
Standard Part ◽  
Full Structure

AbstractIn this paper it is shown that the construction of measures on standard spaces via Loeb measures and the standard part map does not depend on the full structure of the internal algebra being used. A characterization of universal Loeb measurability is given for completely regular Hausdorff spaces, and the behavior of this property under various topological operations is investigated.

On an elementary characterization of the increasing convex ordering, by an application

1994 ◽  
Vol 31 (3) ◽  
pp. 834-840 ◽  
Author(s):  
Armand M. Makowski
Keyword(s):  
Short Proof ◽  
Probability Distributions ◽  
Short Note ◽  
Comparison Result ◽  
Convex Ordering ◽  
Simple Characterization ◽  
Increasing Convex Ordering ◽  
Elementary Characterization

In this short note, we present a simple characterization of the increasing convex ordering on the set of probability distributions on ℝ. We show its usefulness by providing a very short proof of a comparison result for M/GI/1 queues due to Daley and Rolski, and obtained by completely different means.

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