Quasi-multipliers on topological semigroups and their Stone–Čech compactification

2021 ◽  
pp. 2250148
Author(s):  
A. Alinejad ◽  
M. Essmaili ◽  
M. Rostami
Keyword(s):  
Topological Semigroup ◽  
Extra Condition ◽  
Topological Semigroups

In this paper, we introduce and study the notion of quasi-multipliers on a semi-topological semigroup [Formula: see text]. The set of all quasi-multipliers on [Formula: see text] is denoted by [Formula: see text]. First, we study the problem of extension of quasi-multipliers on topological semigroups to its Stone–Čech compactification. Indeed, we prove if [Formula: see text] is a topological semigroup such that [Formula: see text] is pseudocompact, then [Formula: see text] can be regarded as a subset of [Formula: see text] Moreover, with an extra condition we describe [Formula: see text] as a quotient subsemigroup of [Formula: see text] Finally, we investigate quasi-multipliers on topological semigroups, its relationship with multipliers and give some concrete examples.

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.

Algebras of measures on C-distinguished topological semigroups

1978 ◽  
Vol 84 (2) ◽  
pp. 323-336 ◽  
Author(s):  
H. A. M. Dzinotyiweyi
Keyword(s):  
Total Variation ◽  
Topological Semigroup ◽  
Continuous Mapping ◽  
Continuous Functions ◽  
Compact Set ◽  
Locally Compact ◽  
Radon Measures ◽  
Topological Semigroups ◽  
Bounded Complex ◽  
Complex Valued

Let S be a (jointly continuous) topological semigroup, C(S) the set of all bounded complex-valued continuous functions on S and M (S) the set of all bounded complex-valued Radon measures on S. Let (S) (or (S)) be the set of all µ ∈ M (S) such that x → │µ│ (x-1C) (or x → │µ│(Cx-1), respectively) is a continuous mapping of S into ℝ, for every compact set C ⊆ S, and . (Here │µ│ denotes the measure arising from the total variation of µ and the sets x-1C and Cx-1 are as defined in Section 2.) When S is locally compact the set Ma(S) was studied by A. C. and J. W. Baker in (1) and (2), by Sleijpen in (14), (15) and (16) and by us in (3). In this paper we show that some of the results of (1), (2), (14) and (15) remain valid for certain non-locally compact S and raise some new problems for such S.

scholarly journals The cardinality of the set of left invariant means on topological semigroups

1988 ◽  
Vol 37 (2) ◽  
pp. 247-262 ◽  
Author(s):  
Heneri A.M. Dzinotyiweyi
Keyword(s):  
Large Class ◽  
Topological Semigroup ◽  
Continuous Functions ◽  
Upper Bounds ◽  
Compact Sets ◽  
Lower And Upper Bounds ◽  
Topological Semigroups ◽  
Invariant Means ◽  
Uniformly Continuous

For a very large class of topological semigroups, we establish lower and upper bounds for the cardinality of the set of left invariant means on the space of left uniformly continuous functions. In certain cases we show that such a cardinality is exactly , where b is the smallest cardinality of the covering of the underlying topological semigroup by compact sets.

Topological semigroups and their prequantale models

Filomat ◽  
2017 ◽  
Vol 31 (19) ◽  
pp. 6205-6210 ◽  
Author(s):  
Bin Zhao ◽  
Changchun Xia ◽  
Kaiyun Wang
Keyword(s):  
Topological Semigroup ◽  
Satisfying Condition ◽  
Locally Compact ◽  
Topological Semigroups

In this paper, we introduce a condition (?) on topological semigroups, and prove that every T1 topological semigroup satisfying condition (?) has a bounded complete algebraic prequantale model. On the basis of this result, we also show that every T0 topological semigroup satisfying condition (?) can be embedded into a compact and locally compact sober topological semigroup.

scholarly journals On Maximal Ideals of Compact Connected Topological Semigroups

2010 ◽  
Vol 2010 ◽  
pp. 1-5
Author(s):  
Phoebe McLaughlin ◽  
Shing S. So ◽  
Haohao Wang
Keyword(s):  
Topological Semigroup ◽  
Topological Semigroups ◽  
Maximal Ideals ◽  
Compact Topological Semigroup

Several results concerning ideals of a compact topological semigroup with can be found in the literature. In this paper, we further investigate in a compact connected topological semigroup how the conditions and affect the structure of ideals of , especially the maximal ideals.

Concerning Binary Relations on Connected Ordered Spaces

1959 ◽  
Vol 11 ◽  
pp. 107-111 ◽  
Author(s):  
I. S. Krule
Keyword(s):  
Topological Semigroup ◽  
Unit Interval ◽  
General Nature ◽  
Topological Spaces ◽  
Binary Relations ◽  
Real Numbers ◽  
Topological Semigroups ◽  
Ordered Space

In a recent paper Mostert and Shields (4) showed that if a space homeomorphic to the non-negative real numbers is a certain type of topological semigroup, then the semigroup must be that of the non-negative real numbers with the usual multiplication. Somewhat earlier Faucett (2) showed that if a compact connected ordered space is a suitably restricted topological semigroup, then it must be both topologically and algebraically the same as the unit interval of real numbers with its usual multiplication.In studying certain binary relations on topological spaces there have become known (see, in particular, Wallace (5) and the author (3)) a number of properties analogous to those possessed by topological semigroups. Because of these analogous properties between relations and semigroups the author was motivated by the general nature of the Faucett and Mostert-Shields results (that is, that the multiplication assumed turned out to be the same as the usual multiplication) to feel that certain relations on a connected ordered space should turn out to be the same as the orders whose order topologies are the topology on the space.

Continuity of the Inverse in Pseudocompact Paratopological Groups

2007 ◽  
Vol 14 (01) ◽  
pp. 167-175 ◽  
Author(s):  
S. Romaguera ◽  
M. Sanchis
Keyword(s):  
Topological Group ◽  
Topological Semigroup ◽  
Topological Semigroups ◽  
Compact Topological Semigroup ◽  
Paratopological Group ◽  
Bitopological Spaces

By a celebrated theorem of Numakura, a Hausdorff compact topological semigroup with two-sided cancellation is a group which has inverse continuous, i.e., it is a topological group. We improve Numakura's Theorem in the realm of non-Hausdorff topological semigroups. This improvement together with some properties of pseudocompact nature in the field of bitopological spaces is used in order to prove that a T0 paratopological group (G,τ) is a (Hausdorff) pseudocompact topological group if and only if (G, τ ∨ τ-1) is pseudocompact or, equivalently, G is Gδ-dense in the Stone–Čech bicompactification [Formula: see text] of (G, τ, τ-1). We also present a version for paratopological groups of the renowned Comfort–Ross Theorem stating that a topological group is pseudocompact if and only if its Stone–Čech compactification is a topological group.

scholarly journals Commutative Topological Semigroups Embedded into Topological Abelian Groups

Axioms ◽  
2020 ◽  
Vol 9 (3) ◽  
pp. 87
Author(s):  
Julio César Hernández Arzusa
Keyword(s):  
Topological Group ◽  
Abelian Group ◽  
Topological Semigroup ◽  
Abelian Groups ◽  
Sufficient Conditions ◽  
Locally Compact ◽  
Topological Abelian Group ◽  
Topological Semigroups ◽  
Topological Monoid

In this paper, we give conditions under which a commutative topological semigroup can be embedded algebraically and topologically into a compact topological Abelian group. We prove that every feebly compact regular first countable cancellative commutative topological semigroup with open shifts is a topological group, as well as every connected locally compact Hausdorff cancellative commutative topological monoid with open shifts. Finally, we use these results to give sufficient conditions on a commutative topological semigroup that guarantee it to have countable cellularity.

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 Retraction of the paper entitled “Lepton number violation in a unified framework“

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Apriadi Salim Adam ◽  
Yuta Kawamura ◽  
Yamato Matsuo ◽  
Takuya Morozumi ◽  
Yusuke Shimizu ◽  
...  
Keyword(s):  
Mass Function ◽  
Lepton Number ◽  
Primordial Black Hole ◽  
Unified Framework ◽  
Extra Condition ◽  
Formal Expression ◽  
Lepton Number Violation ◽  
Standard Criterion ◽  
New Criterion ◽  
New Formula

Abstract Computations of the primordial black hole (PBH) mass function discussed in the literature have conceptual issues. They stem from the fact that the mass function is a differential quantity and the standard criterion of the PBH formation from the seed primordial fluctuations cannot be directly applied to the computation of the differential quantities. We propose a new criterion of the PBH formation, which is the addition of one extra condition to the existing one. By doing this, we derive a formal expression of the PBH mass function without introducing any ambiguous interpretations that exist in the previous studies. Once the underlying primordial fluctuations are specified, the PBH mass function can be in principle determined by the new formula. As a demonstration of our formulation, we compute the PBH mass function analytically for the case where the perturbations are Gaussian and the space is 1 dimension.

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