共查询到20条相似文献,搜索用时 15 毫秒
1.
By means of the theory of bispaces we show that a countably compact T0 paratopological group (G, τ) is a topological group if and only if (G, τ ∨ τ-1) is ω-bounded (here τ-1 is the conjugate topology of τ). Our approach is premised on the fact that every paratopological countably compact paratopological
group is a Baire space and on the notion of a 2-pseudocompact space. We also prove that every ω-bounded (respectively, topologically
periodic) Baire paratopological group admits a weaker Hausdorff group topology. In particular, ω-bounded (respectively, topologically
periodic) 2-pseudocompact (so, also countably compact) paratopological groups enjoy this property. Some topological properties
turning countably compact topological semigroups into topological groups are presented and some open questions are posed. 相似文献
2.
John F. Berglund 《Semigroup Forum》1972,5(1):191-215
An inverse Clifford Semigroup is a semilattice of groups. Conditions are given for constructing a compact semitopological
(separately continuous multiplication) inverse Clifford semigroup on a compact Hausdorff semilattice. The conditions are necessary
and sufficient for decomposing a compact inverse Clifford semigroup containing a dense subgroup and locally compact maximal
groups into its semilattice of groups. A catalogue of examples is given to demonstrate the construction while exhibiting various
pathologies.
This work was supported in part by the S.R.C. 相似文献
3.
Oleg Pavlov 《Proceedings of the American Mathematical Society》2001,129(9):2771-2775
We construct an example of a normal countably compact not absolutely countably compact space. We also prove that every hereditarily normal countably compact space is absolutely countably compact and suggest a method for construction of hereditarily normal spaces without property .
4.
We search for conditions on a countably compact (pseudocompact) topological semigroup under which: (i) each maximal subgroup
H(e) in S is a (closed) topological subgroup in S; (ii) the Clifford part H(S) (i.e. the union of all maximal subgroups) of the semigroup S is a closed subset in S; (iii) the inversion inv: H(S) → H(S) is continuous; and (iv) the projection π: H(S) → E(S), π: x ↦ xx
−1, onto the subset of idempotents E(S) of S, is continuous.
相似文献
5.
We show that if S is a countably infinite right cancellative semigroup and T is an infinite compact set of idempotents in the Stone–?ech compactification \(\beta S\) of S, then T contains an infinite compact left zero semigroup. 相似文献
6.
A semigroup S is called a Clifford semigroup if it is completely regular and inverse. In this paper, some relations related to the least
Clifford semigroup congruences on completely regular semigroups are characterized. We give the relation between Y and ξ on completely regular semigroups and get that Y
* is contained in the least Clifford congruence on completely regular semigroups generally. Further, we consider the relation
Y
*, Y, ν and ε on completely simple semigroups and completely regular semigroups.
This work is supported by Leading Academic Discipline Project of Shanghai Normal University, Project Number: DZL803 and General
Scientific Research Project of Shanghai Normal University, No. SK200707. 相似文献
7.
S. Spadaro 《Acta Mathematica Hungarica》2016,149(1):254-262
The weak Whyburn property is a generalization of the classical sequential property that was studied by many authors. A space X is weakly Whyburn if for every non-closed set \({A \subset X}\) there is a subset \({B \subset A}\) such that \({\overline{B} \setminus A}\) is a singleton. We prove that every countably compact Urysohn space of cardinality smaller than the continuum is weakly Whyburn and show that, consistently, the Urysohn assumption is essential. We also give conditions for a (countably compact) weakly Whyburn space to be pseudoradial and construct a countably compact weakly Whyburn non-pseudoradial regular space, which solves a question asked by Angelo Bella in private communication. 相似文献
8.
On the infinite semigroup of matrix units
there exists no semigroup compact [countably compact] topology.
Any continuous homomorphism from the infinite topological
semigroup of matrix units into a compact topological semigroup is
annihilating. The semigroup of matrix units is algebraically
h-closed in the class of topological inverse semigroups. Some
H-closed minimal semigroup topologies on the infinite semigroup
of matrix units are considered. 相似文献
9.
10.
In Billhardt et al. (Semigroup Forum 79:101–118, 2009) the authors introduced the notion of an associate inverse subsemigroup of a regular semigroup, extending the concept of an associate subgroup of a regular semigroup, first presented in Blyth et al. (Glasgow Math. J. 36:163–171, 1994). The main result of the present paper, Theorem 2.15, establishes that a regular semigroup S with an associate inverse subsemigroup S ? satisfies three simple identities if and only if it is isomorphic to a generalised Rees matrix semigroup M(T;A,B;P), where T is a Clifford semigroup, A and B are bands, with common associate inverse subsemigroup E(T) satisfying the referred identities, and P is a sandwich matrix satisfying some natural conditions. If T is a group and A, B are left and right zero semigroups, respectively, then the structure described provides a usual Rees matrix semigroup with normalised sandwich matrix, thus generalising the Rees matrix representation for completely simple semigroups. 相似文献
11.
含幺Clifford半群上的Rees矩阵半群的同余和正规加密群结构 总被引:1,自引:0,他引:1
给出了含幺Clifford半群上的Rees矩阵半群S的正规加密群结构,证明了在含幺Clifford半群上的Rees矩阵半群S上以下两个条件是等价的:(1)S上的同余ρ是完全单半群同余;(2)S上的同余ρ和S上的相容组之间存在保序双射.最后还证明了S上的完全单半群同余所构成的同余格是半模的. 相似文献
12.
Bernd Billhardt 《Semigroup Forum》2005,70(2):243-251
A regular (inverse) semigroup S is called F-regular (F-inverse), if each class of the least group congruence S contains a greatest element with respect to the natural partial order on S. Such a semigroup is necessarily an E-unitary regular (hence orthodox) monoid. We show that each F-regular semigroup S is isomorphic to a well determined subsemigroup of a semidirect product of a band X by S/S, where X belongs to the band variety, generated by the band of idempotents ES of S. Our main result, Theorem 4, is the regular version of the corresponding fact for inverse semigroups, and might be useful to generalize further features of the theory of F-inverse semigroups to the F-regular case. 相似文献
13.
For a large class of locally compact semitopological semigroups S, the Stone-Čech compactification β
S is a semigroup compactification if and only if S is either discrete or countably compact. Furthermore, for this class of semigroups which are neither discrete nor countably
compact, the quotient
contains a linear isometric copy of ℓ
∞. These results improve theorems by Baker and Butcher and by Dzinotyiweyi. 相似文献
14.
Mary Ellen Rudin Ian S. Stares Jerry E. Vaughan 《Proceedings of the American Mathematical Society》1997,125(3):927-934
We show that every countably compact space which is monotonically normal, almost 2-fully normal, radial , or with countable spread is absolutely countably compact. For the first two mentioned properties, we prove more general results not requiring countable compactness. We also prove that every monotonically normal, orthocompact space is finitely fully normal.
15.
R. Exel 《Semigroup Forum》2009,79(1):159-182
By a Boolean inverse semigroup we mean an inverse semigroup whose semilattice of idempotents is a Boolean algebra. We study representations of a given inverse
semigroup
in a Boolean inverse semigroup which are tight in a certain well defined technical sense. These representations are supposed to preserve as much as possible any trace of
Booleanness present in the semilattice of idempotents of
. After observing that the Vagner–Preston representation is not tight, we exhibit a canonical tight representation for any
inverse semigroup with zero, called the regular tight representation. We then tackle the question as to whether this representation is faithful, but it turns out that the answer is often negative.
The lack of faithfulness is however completely understood as long as we restrict to continuous inverse semigroups, a class generalizing the E
*-unitaries.
Partially supported by CNPq. 相似文献
16.
We establish topological properties of the symmetric inverse topological semigroup of finite transformations
of the rank ≤ n. We show that the topological inverse semigroup
is algebraically h -closed in the class of topological inverse semigroups. Also we prove that a topological semigroup S with countably compact square S×S does not contain the semigroup
for infinite cardinal λ and show that the Bohr compactification of an infinite topological symmetric inverse semigroup of
finite transformations
of the rank ≤ n is the trivial semigroup. 相似文献
17.
S. Garcia-Ferreira A. H. Tomita S. Watson 《Proceedings of the American Mathematical Society》2005,133(3):937-943
We prove that the existence of a selective ultrafilter on implies the existence of a countably compact group without non-trivial convergent sequences all of whose powers are countably compact. Hence, by using a selective ultrafilter on , it is possible to construct two countably compact groups without non-trivial convergent sequences whose product is not countably compact.
18.
We study properties of continuous homomorphisms
from β S into T* and
from S* into T*, where S denotes a countably
infinite semigroup and T denotes a countably infinite
group. We show that they have striking algebraic properties
if they do not arise as continuous
extensions of homomorphisms from S to T. 相似文献
19.
Approximate Identities in Spaces of all
Absolutely Continuous Measures on Locally Compact Semigroups
Let G be a locally compact group. Then Ma (G), the space of all absolutely continuous measures on G, has a bounded
approximate identity. Baker and Baker proved that (S) (the space of all measures M(S) so that maps x x *|| and x ||*x are weak continuous from a locally compact semigroup S into M(S)) is closed under absolutely continuity and has an approximate identity. The main purpose of this paper is to show that similar results hold true for a locally compact semigroup S and Ma(S) the space of all absolutely continuous measures on S. 相似文献
20.
S. Sundar 《Semigroup Forum》2013,86(2):383-394
In this article, we prove that the inverse semigroup associated to the Cuntz-Li relations is strongly 0-E unitary and is an F ?-inverse semigroup. We also identify the universal group of the inverse semigroup. This gives a conceptual explanation for the result obtained in S. Sundar (arXiv:1201.4620v1, 2012). 相似文献