On the dual semigroups of compact semigroups

2017 ◽  
Vol 13 (2) ◽  
Author(s):  
A. Pol
Keyword(s):  
Compact Semigroups

scholarly journals H cross-sections in J-classes of compact semigroups

1973 ◽  
Vol 3 (3) ◽  
pp. 281-286
Author(s):  
J.R. Goodwin
Keyword(s):  
Cross Sections ◽  
Compact Semigroups

Idempotents in compact semigroups and Ramsey theory

1989 ◽  
Vol 68 (3) ◽  
pp. 257-270 ◽  
Author(s):  
H. Furstenberg ◽  
Y. Katznelson
Keyword(s):  
Ramsey Theory ◽  
Compact Semigroups

scholarly journals Skew compact semigroups

2003 ◽  
Vol 4 (1) ◽  
pp. 133
Author(s):  
Ralph D. Kopperman ◽  
Desmond Robbie
Keyword(s):  
Continuous Semigroup ◽  
Minimal Ideal ◽  
Compact Semigroup ◽  
Closed Ideal ◽  
Hausdorff Spaces ◽  
Compact Spaces ◽  
Compact Semigroups ◽  
Compact Topology ◽  
Hausdorff Group ◽  
Non Hausdorff Spaces

<p>Skew compact spaces are the best behaving generalization of compact Hausdorff spaces to non-Hausdorff spaces. They are those (X ; τ ) such that there is another topology τ* on X for which τ V τ* is compact and (X; τ ; τ*) is pairwise Hausdorff; under these conditions, τ uniquely determines τ *, and (X; τ*) is also skew compact. Much of the theory of compact T<sub>2</sub> semigroups extends to this wider class. We show:</p> <p>A continuous skew compact semigroup is a semigroup with skew compact topology τ, such that the semigroup operation is continuous τ<sup>2</sup>→ τ. Each of these contains a unique minimal ideal which is an upper set with respect to the specialization order.</p> <p>A skew compact semigroup which is a continuous semigroup with respect to both topologies is called a de Groot semigroup. Given one of these, we show:</p> <p>It is a compact Hausdorff group if either the operation is cancellative, or there is a unique idempotent and S<sup>2</sup> = S.</p> <p>Its topology arises from its subinvariant quasimetrics.</p> <p>Each *-closed ideal ≠ S is contained in a proper open ideal.</p>

scholarly journals On the existence of invariant measures on certain types of compact semigroups

1957 ◽  
Vol 07 (2) ◽  
pp. 165-182 ◽  
Author(s):  
Štefan Schwarz
Keyword(s):  
Invariant Measures ◽  
Compact Semigroups

scholarly journals Monotone Homomorphisms of Compact Semigroups

1969 ◽  
Vol 9 (1-2) ◽  
pp. 167-175
Author(s):  
C. E. Clark
Keyword(s):  
Homomorphic Image ◽  
Topological Semigroups ◽  
Compact Semigroups

The problem of determining the class of homomorphic images of a given class of topological semigroups seems to have received little attention in the literature. In [4] Cohen and Krule determined the homomorphic images of a semigroup with zero on an interval. Anderson and Hunter in [1] proved several theorems in this direction. In general, the problem seems to be rather difficult. However, the difficulty is lessened somewhat if all of the homomorphisms of the semigroups in question must be monotone. Phillips, [7], showed that every homomorphism of a standard thread is monotone and hence every homomorphic image of a standard thread is either a standard thread or a point. In this paper a larger class of topological semigroups which admit only monotone homomorphisms is given. These results are used to determine the topological nature of the homomorphic images of certain classes of topological semigroups. These include products of standard threads with min threads, certain semilattices on a two-cell, and compact connected lattices in the plane.

On summability of pairs of convolution sequences of probability measures on locally compact semigroups

1998 ◽  
Vol 47 (3) ◽  
pp. 481-492
Author(s):  
Cvetan Jardas ◽  
Josip Pečarić ◽  
Nikola Sarapa
Keyword(s):  
Probability Measures ◽  
Locally Compact ◽  
Compact Semigroups ◽  
Locally Compact Semigroups

The structure of compact semigroups

1978 ◽  
pp. 28-90
Author(s):  
John F. Berglund ◽  
Hugo D. Junghenn ◽  
Paul Milnes
Keyword(s):  
Compact Semigroups

On the Semigroup of Probability Measures of a Locally Compact Semigroup II

1987 ◽  
Vol 30 (3) ◽  
pp. 273-281 ◽  
Author(s):  
James C. S. Wong
Keyword(s):  
Convex Sets ◽  
Compact Convex ◽  
Compact Semigroup ◽  
Probability Measures ◽  
Locally Compact ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Fixed Point Properties ◽  
The Relationship ◽  
Locally Compact Semigroups

AbstractThis is a sequel to the author's paper "On the semigroup of probability measures of a locally compact semigroup." We continue to investigate the relationship between amenability of spaces of functions and functionals associated with a locally compact semigroups S and its convolution semigroup MO(S) of probability measures and fixed point properties of actions of S and MO(S) on compact convex sets.

scholarly journals Essentially coercive forms and asymptotically compact semigroups

2020 ◽  
Vol 491 (2) ◽  
pp. 124318 ◽  
Author(s):  
W. Arendt ◽  
I. Chalendar
Keyword(s):  
Compact Semigroups

scholarly journals On when a topologically simple semigroup is simple

1978 ◽  
Vol 26 (1) ◽  
pp. 126-128
Author(s):  
Kermit Sigmon
Keyword(s):  
Open Problem ◽  
Simple Semigroup ◽  
Infinite Order ◽  
Compact Semigroup ◽  
Subject Classification ◽  
Locally Compact ◽  
M 10 ◽  
Compact Semigroups ◽  
20 M 10

AbstractThe compact semigroups in which each topologically simple subsemigroup is simple are characterized as those in which no subgroup sontains an element of infinite order. It is also shown that a locally compact toplogically simple subsemigroup of a compact semigroup must be simple. The note closes with an open problem.Subject classification (Amer. Math. Soc. (MOS) 1970): primary 22 A 15; secondary 20 M 10.

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