scholarly journals A universal semigroup

1971 ◽  
Vol 4 (2) ◽  
pp. 159-161
Author(s):  
Sidney A. Morris
Keyword(s):  
Metric Semigroup ◽  
Universal Semigroup

J.H. Michael recently proved that there exists a metric semigroup U such that every compact metric semigroup with property P is topologically isomorphic to a subsemigroup of U; where a semigroup S has property P if and only if for each x, y in S, x ≠ y, there is a z in S such that xs ≠ yz or zx ≠ zyA stronger result is proved here more simply. It is shown that for any set A of metric semigroups there exists a metric semigroup U such that each S in A is topologically isomorphic to a subsemigroup of U. In particular this is the case when A is the class of all separable metric semigroups, or more particularly the class of all compact metric semigroups.

scholarly journals A universal semigroup

1970 ◽  
Vol 11 (2) ◽  
pp. 216-220 ◽  
Author(s):  
J. H. Michael
Keyword(s):  
Related Result ◽  
Compact Semigroup ◽  
Linear Operators ◽  
Hilbert Cube ◽  
Bounded Linear ◽  
Usual Norm ◽  
Compact Topological Semigroup ◽  
Countably Infinite ◽  
Metric Semigroup ◽  
Universal Semigroup

In [4] S. Ulam asks the following question. ‘Does there exist a universal compact semigroup; i.e., a semigroup U such that every compact topological semigroup is continuously isomorphic to a subsemigroup of it?’ The author has not been able to answer this question. However, in this paper, a proof is given for the following related result.Let Q denote the Hilbert cube of countably infinite dimension and C(Q) the Banach space of continuous real-valued functions on Q with the usual norm. Let U denote the semigroup consisting of all bounded linear operators T: C(Q)→ C(Q) with ∥T∥ ≦ 1 and let U be endowed with the strong topology. Then, for every compact metric semigroup S with the property: (1.1) for all x, y ∈ S, with x ≠ y, there exists a z ∈ S, such that xz ≠ yz or zx ≠ zy;there exists a 1 − 1 mapping φ of S into U such that φ is both a semigroup isomorphism and a homeomorphism.U is metrizable, but is not compact; hence it does not provide an answer to the question of Ulam. The proof of the above statement leans heavily on a result of S. Kakutani [1].

A universal semigroup

1970 ◽  
Vol 9 (6) ◽  
pp. 442-446
Author(s):  
D. J. Collins
Keyword(s):  
Universal Semigroup

Strongly alg-universal semigroup varieties

1999 ◽  
Vol 42 (1-2) ◽  
pp. 79-105
Author(s):  
V. Koubek ◽  
J. Sichler
Keyword(s):  
Semigroup Varieties ◽  
Universal Semigroup

scholarly journals Some algebraic universal semigroup compactifications

2001 ◽  
Vol 26 (6) ◽  
pp. 353-357
Author(s):  
H. R. Ebrahimi-Vishki
Keyword(s):  
Semigroup Compactifications ◽  
Function Algebras ◽  
Universal Semigroup

Universal compactifications of semitopological semigroups with respect to the properties satisfying the varieties of semigroups and groups are studied through two function algebras.

scholarly journals On Helly's principle for metric semigroup valued BV mappings to two real variables

2002 ◽  
Vol 66 (2) ◽  
pp. 245-257 ◽  
Author(s):  
M. Balcerzak ◽  
S. A. Belov ◽  
V. V. Chistyakov
Keyword(s):  
Hardy Space ◽  
Total Variation ◽  
Metric Space ◽  
Convergent Sequence ◽  
Translation Invariant ◽  
Selection Principle ◽  
Additive Semigroup ◽  
Type Selection ◽  
Metric Semigroup ◽  
Uniformly Bounded

We introduce a concept of metric space valued mappings of two variables with finite total variation and define a counterpart of the Hardy space. Then we establish the following Helly type selection principle for mappings of two variables: Let X be a metric space and a commutative additive semigroup whose metric is translation invariant. Then an infinite pointwise precompact family of X-valued mappings on the closed rectangle of the plane, which is of uniformly bounded total variation, contains a pointwise convergent sequence whose limit is a mapping with finite total variation.

scholarly journals A note on conservative measures on semigroups

1992 ◽  
Vol 15 (1) ◽  
pp. 195-198
Author(s):  
N. A. Tserpes
Keyword(s):  
Ergodic Theory ◽  
Measure Space ◽  
Borel Measure ◽  
Left Group ◽  
Closed Mappings ◽  
Metric Semigroup

Consider(S,B,μ)the measure space whereSis a topological metric semigroup andμa countably additive bounded Borel measure. Callμconservative if all right translationstx:s→sx,x∈S(which are assumed closed mappings) are conservative with respect(S,B,μ)in the ergodic theory sense. It is shown that the semigroup generated by the support ofμis a left group. An extension of this result is obtained forσ-finiteμ.

scholarly journals Universal varieties of semigroups

1984 ◽  
Vol 36 (2) ◽  
pp. 143-152 ◽  
Author(s):  
V. Koubek ◽  
J. Sichler
Keyword(s):  
Full Subcategory ◽  
Semigroup Variety ◽  
Endomorphism Monoid ◽  
Commutative Semigroups ◽  
Universal Semigroup

AbstractA category V is called universal (or binding) if every category of algebras is isomorphic to a full subcategory of V. The main result states that a semigroup variety V is universal if and only if it contains all commutative semigroups and fails the identity xnyn = (xy)n for every n ≥ 1. Further-more, the universality of a semigroup variety V is equivalent to the existence in V of a nontrivial semigroup whose endomorphism monoid is trivial, and also to the representability of every monoid as the monoid of all endomorphisms of some semigroup in V. Every universal semigroup variety contains a minimal one with this property while there is no smallest universal semigroup variety.

Separating Points of βℕ By Minimal Flows

1994 ◽  
Vol 46 (4) ◽  
pp. 758-771 ◽  
Author(s):  
Neil Hindman ◽  
Jimmie Lawson ◽  
Amha Lisan
Keyword(s):  
Characteristic Function ◽  
Topological Semigroup ◽  
Semigroup Compactification ◽  
Enveloping Semigroup ◽  
Smallest Ideal ◽  
Universal Semigroup

AbstractWe consider minimal left ideals L of the universal semigroup compactification of a topological semigroup S. We show that the enveloping semigroup of L is homeomorphically isomorphic to if and only if given q ≠ r in , there is some p in the smallest ideal of with qp ≠ rp. We derive several conditions, some involving minimal flows, which are equivalent to the ability to separate q and r in this fashion, and then specialize to the case that S = , and the compactification is . Included is the statement that some set A whose characteristic function is uniformly recurrent has .

The universal semigroup of relations

1979 ◽  
Vol 2 (2) ◽  
pp. 91-117 ◽  
Author(s):  
John Paul Boyd
Keyword(s):  
Universal Semigroup

scholarly journals A pointwise selection principle for metric semigroup valued functions

2008 ◽  
Vol 341 (1) ◽  
pp. 613-625 ◽  
Author(s):  
Vyacheslav V. Chistyakov ◽  
Caterina Maniscalco
Keyword(s):  
Selection Principle ◽  
Metric Semigroup
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