scholarly journals On locally compact topological graph inverse semigroups

2019 ◽  
Vol 267 ◽  
pp. 106873 ◽  
Author(s):  
Serhii Bardyla
Keyword(s):  
Inverse Semigroups ◽  
Topological Graph ◽  
Locally Compact

scholarly journals Embedding inverse semigroups of homeomorphisms on closed subsets

1977 ◽  
Vol 18 (2) ◽  
pp. 199-207 ◽  
Author(s):  
Bridget Bos Baird
Keyword(s):  
Topological Space ◽  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Topological Spaces ◽  
Locally Compact ◽  
Compact Metric Space ◽  
Countable Space ◽  
The One ◽  
One Point Compactification ◽  
First Countable Space

All topological spaces here are assumed to be T2. The collection F(Y)of all homeomorphisms whose domains and ranges are closed subsets of a topological space Y is an inverse semigroup under the operation of composition. We are interested in the general problem of getting some information about the subsemigroups of F(Y) whenever Y is a compact metric space. Here, we specifically look at the problem of determining those spaces X with the property that F(X) is isomorphic to a subsemigroup of F(Y). The main result states that if X is any first countable space with an uncountable number of points, then the semigroup F(X) can be embedded into the semigroup F(Y) if and only if either X is compact and Y contains a copy of X, or X is noncompact and locally compact and Y contains a copy of the one-point compactification of X.

scholarly journals Topological graph inverse semigroups

2016 ◽  
Vol 208 ◽  
pp. 106-126 ◽  
Author(s):  
Z. Mesyan ◽  
J.D. Mitchell ◽  
M. Morayne ◽  
Y.H. Péresse
Keyword(s):  
Inverse Semigroups ◽  
Topological Graph

scholarly journals Group actions on topological graphs

2011 ◽  
Vol 32 (5) ◽  
pp. 1527-1566 ◽  
Author(s):  
VALENTIN DEACONU ◽  
ALEX KUMJIAN ◽  
JOHN QUIGG
Keyword(s):  
Compact Group ◽  
Universal Covering ◽  
Locally Compact Group ◽  
Skew Product ◽  
Topological Graph ◽  
Topological Graphs ◽  
Locally Compact ◽  
Natural Action ◽  
Morita Equivalent ◽  
Dual Action

AbstractWe define the action of a locally compact groupGon a topological graphE. This action induces a natural action ofGon theC*-correspondence ℋ(E) and on the graphC*-algebraC*(E). If the action is free and proper, we prove thatC*(E)⋊rGis strongly Morita equivalent toC*(E/G) . We define the skew product of a locally compact groupGby a topological graphEvia a cocyclec:E1→G. The group acts freely and properly on this new topological graphE×cG. IfGis abelian, there is a dual action onC*(E) such that$C^*(E)\rtimes \hat {G}\cong C^*(E\times _cG)$. We also define the fundamental group and the universal covering of a topological graph.

scholarly journals RECOVERING THE BOUNDARY PATH SPACE OF A TOPOLOGICAL GRAPH USING POINTLESS TOPOLOGY

2020 ◽  
pp. 1-17
Author(s):  
GILLES G. DE CASTRO
Keyword(s):  
Path Space ◽  
Topological Graph ◽  
Topological Graphs ◽  
Locally Compact ◽  
C Algebra ◽  
Compact Spaces ◽  
Compact Topology ◽  
Boundary Path ◽  
Definition Of ◽  
Locally Compact Spaces

First, we generalize the definition of a locally compact topology given by Paterson and Welch for a sequence of locally compact spaces to the case where the underlying spaces are $T_{1}$ and sober. We then consider a certain semilattice of basic open sets for this topology on the space of all paths on a graph and impose relations motivated by the definitions of graph C*-algebra in order to recover the boundary path space of a graph. This is done using techniques of pointless topology. Finally, we generalize the results to the case of topological graphs.

scholarly journals An algebraic characterisation of ample type I groupoids

2021 ◽  
Author(s):  
Gabriel Favre ◽  
Sven Raum
Keyword(s):  
Inverse Semigroup ◽  
Inverse Semigroups ◽  
Type I ◽  
Locally Compact

AbstractWe give algebraic characterisations of the type I and CCR properties for locally compact second countable, ample Hausdorff groupoids in terms of subquotients of its Boolean inverse semigroup of compact open local bisections. It yields in turn algebraic characterisations of both properties for inverse semigroups with meets in terms of subquotients of their Booleanisation.

Locally compact bisimple inverse semigroups

1981 ◽  
Vol 22 (1) ◽  
pp. 387-389 ◽  
Author(s):  
Kadir R. Ahre
Keyword(s):  
Inverse Semigroups ◽  
Locally Compact

ON A GROUPOID CONSTRUCTION FOR ACTIONS OF CERTAIN INVERSE SEMIGROUPS

1994 ◽  
Vol 05 (03) ◽  
pp. 349-372 ◽  
Author(s):  
ALEXANDRU NICA
Keyword(s):  
Inverse Semigroup ◽  
Compact Space ◽  
Transformation Group ◽  
Algebraic Theory ◽  
Inverse Semigroups ◽  
Discrete Groups ◽  
Crossed Products ◽  
Locally Compact ◽  
Locally Compact Space ◽  
The One

We consider a version of the notion of F-inverse semigroup (studied in the algebraic theory of inverse semigroups). We point out that an action of such an inverse semigroup on a locally compact space has associated a natural groupoid construction, very similar to the one of a transformation group. We discuss examples related to Toeplitz algebras on subsemigroups of discrete groups, to Cuntz-Krieger algebras, and to crossed-products by partial automorphisms in the sense of Exel.

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