On the immersion of topological semigroups in topological groups

1969 ◽  
Vol 6 (4) ◽  
pp. 697-701
Author(s):  
L. B. Shneperman
Keyword(s):  
Topological Groups ◽  
Topological Semigroups

On the Dimension Modulo Classes of Topological Spaces and Free Topological Groups

2003 ◽  
Vol 10 (2) ◽  
pp. 209-222
Author(s):  
I. Bakhia
Keyword(s):  
Wide Class ◽  
Sufficient Conditions ◽  
Topological Spaces ◽  
Topological Groups ◽  
Compact Spaces ◽  
Topological Semigroups

Abstract Functions of dimension modulo a (rather wide) class of spaces are considered and the conditions are found, under which the dimension of the product of spaces modulo these classes is equal to zero. Based on these results, the sufficient conditions are established, under which spaces of free topological semigroups (in the sense of Marxen) and spaces of free topological groups (in the sense of Markov and Graev) are zero-dimensional modulo classes of compact spaces.

scholarly journals Certain semigroups embeddabable in topological groups

1982 ◽  
Vol 33 (1) ◽  
pp. 30-39 ◽  
Author(s):  
Heneri A. M. Dzinotyiweyi
Keyword(s):  
Invariant Measures ◽  
Locally Compact Group ◽  
Continuous Measure ◽  
Topological Groups ◽  
Empty Interior ◽  
Locally Compact ◽  
Absolutely Continuous ◽  
Topological Semigroups ◽  
Absolutely Continuous Measure ◽  
Locally Compact Topological Group

AbstractIn this paper we study commutative topological semigroups S admitting an absolutely continuous measure. When S is cancellative we show that S admits a weaker topology J with respect to which (S, J) is embeddable as a subsemigroup with non-empty interior in some locally compact topological group. As a consequence, we deduce certain results related to the existence of invariant measures on S and for a large class of locally compact topological semigroups S, we associate S with some useful topological subsemigroup of a locally compact group.

Representations of Foundation Semigroups and their Algebras

1985 ◽  
Vol 37 (1) ◽  
pp. 29-47 ◽  
Author(s):  
M. Lashkarizadeh Bami
Keyword(s):  
General Theory ◽  
Group Algebra ◽  
Weak Topology ◽  
Compact Semigroup ◽  
Topological Groups ◽  
Locally Compact ◽  
Topological Semigroups ◽  
Locally Compact Semigroup ◽  
Compact Semigroups ◽  
Locally Compact Semigroups

The aim of this paper is to extend to a suitable class of topological semigroups parts of well-defined theory of representations of topological groups. In attempting to obtain these results it was soon realized that no general theory was likely to be obtainable for all locally compact semigroups. The reason for this is the absence of any analogue of the group algebra Ll(G). So the theory in this paper is restricted to a certain family of topological semigroups. In this account we shall only give the details of those parts of proofs which depart from the standard proofs of analogous theorems for groups.On a locally compact semigroup S the algebra of all μ ∊ M(S) for which the mapping and of S to M(S) (where denotes the point mass at x) are continuous when M(S) has the weak topology was first studied in the sequence of papers [1, 2, 3] by A. C. and J. W. Baker.

scholarly journals Embedding topological semigroups in topological groups

1970 ◽  
Vol 17 (2) ◽  
pp. 127-138 ◽  
Author(s):  
Sheila A. McKilligan
Keyword(s):  
Commutative Semigroup ◽  
Algebraic Structure ◽  
Necessary Conditions ◽  
Cancellative Semigroup ◽  
Necessary Condition ◽  
Topological Groups ◽  
Topological Semigroups

If we consider a semigroup, its algebraic structure may be such that it is isomorphic to a subsemigroup of a group, or is algebraically embeddable in a group. This problem was investigated in 1931 by Ore who obtained in (4) a set of necessary conditions for this embedding. A necessary condition is that the semigroup should be cancellative: for any a, x, y in the semigroup either xa = ya or ax = ay implies that x = y. Malcev in (3) showed that this was not sufficient. It is enough to note that his example was a non-commutative semigroup: a commutative cancellative semigroup is embeddable algebraically in a group.

Embedding topological semigroups in topological groups

1970 ◽  
Vol 1 (1) ◽  
pp. 224-231 ◽  
Author(s):  
Francis T. Christoph
Keyword(s):  
Topological Groups ◽  
Topological Semigroups

The Open Mapping and Closed Graph Theorem for Embeddable Topological Semigroups

1975 ◽  
Vol 18 (5) ◽  
pp. 671-674
Author(s):  
Douglass L. Grant
Keyword(s):  
Independent Interest ◽  
Open Mapping ◽  
Topological Groups ◽  
Closed Graph ◽  
Graph Theorem ◽  
Closed Graph Theorem ◽  
Preliminary Results ◽  
Topological Semigroups

Some extensions of the open mapping and closed graph theorem are proved for certain classes of commutative topological semigroups, namely those embeddable as open subsets of topological groups. Preliminary results of independent interest include investigations of properties which “lift” from embeddable semigroups to the groups in which they are embedded, and from semigroup homomorphisms to homomorphisms of the groups.

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