The bohr compactification of a dense ideal in a topological semigroup

1973 ◽  
Vol 6 (1) ◽  
pp. 86-92 ◽  
Author(s):  
J. A. Hildebrant ◽  
J. D. Lawson
Keyword(s):  
Topological Semigroup ◽  
Bohr Compactification ◽  
Dense Ideal

The Bohr compactification, modulo a metrizable subgroup

1993 ◽  
Vol 143 (2) ◽  
pp. 119-136
Author(s):  
W. W. Comfort ◽  
F. Javier Trigos-Arrieta ◽  
Ta-Sun Wu
Keyword(s):  
Bohr Compactification

scholarly journals The translational hull of a topological semigroup

1976 ◽  
Vol 221 (2) ◽  
pp. 251-251 ◽  
Author(s):  
J. A. Hildebrant ◽  
J. D. Lawson ◽  
D. P. Yeager
Keyword(s):  
Topological Semigroup

scholarly journals Quantum Bohr compactification

2005 ◽  
Vol 49 (4) ◽  
pp. 1245-1270 ◽  
Author(s):  
Piotr M. Sołtan
Keyword(s):  
Bohr Compactification

Semidirect Product Compactifications

1983 ◽  
Vol 35 (1) ◽  
pp. 1-32
Author(s):  
F. Dangello ◽  
R. Lindahl
Keyword(s):  
Direct Product ◽  
Semidirect Product ◽  
Topological Semigroup ◽  
Sufficient Conditions ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Topological Semigroups ◽  
Weakly Almost Periodic ◽  
Necessary And Sufficient

1. Introduction. K. Deleeuw and I. Glicksberg [4] proved that if S and T are commutative topological semigroups with identity, then the Bochner almost periodic compactification of S × T is the direct product of the Bochner almost periodic compactifications of S and T. In Section 3 we consider the semidirect product of two semi topological semigroups with identity and two unital C*-subalgebras and of W(S) and W(T) respectively, where W(S) is the weakly almost periodic functions on S. We obtain necessary and sufficient conditions and for a semidirect product compactification of to exist such that this compactification is a semi topological semigroup and such that this compactification is a topological semigroup. Moreover, we obtain the largest such compactifications.

scholarly journals More On the countability index and the density index of S(X)

1990 ◽  
Vol 33 (1) ◽  
pp. 159-164
Author(s):  
K. D. Magill
Keyword(s):  
Finite Number ◽  
Topological Semigroup ◽  
Hausdorff Space ◽  
Extension Property ◽  
Dimensional Subspace ◽  
Countable Subset ◽  
Compact Open Topology ◽  
Locally Compact ◽  
Density Index ◽  
Locally Compact Hausdorff Space

The countability index, C(S), of a semigroup S is the smallest integer n, if it exists, such that every countable subset of S is contained in a subsemigroup with n generators. If no such integer exists, define C(S) = ∞. The density index, D(S), of a topological semigroup S is the smallest integer n, if it exists, such that S contains a dense subsemigroup with n generators. If no such integer exists, define D(S) = ∞. S(X) is the topological semigroup of all continuous selfmaps of the locally compact Hausdorff space X where S(X) is given the compact-open topology. Various results are obtained about C(S(X)) and D(S(X)). For example, if X consists of a finite number (< 1) of components, each of which is a compact N-dimensional subspace of Euclidean Nspace and has the internal extension property and X is not the two point discrete space. Then C(S(X)) exceeds two but is finite. There are additional results for C(S(X)) and similar results for D(S(X)).

scholarly journals Subsemigroups of transitive semigroups

2011 ◽  
Vol 32 (3) ◽  
pp. 1043-1071 ◽  
Author(s):  
ÉTIENNE MATHERON
Keyword(s):  
Topological Space ◽  
Topological Semigroup ◽  
General Conditions

AbstractLet Γ be a topological semigroup acting on a topological space X, and let Γ0 be a subsemigroup of Γ. We give general conditions ensuring that Γ and Γ0 have the same transitive points.

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