nLab
amenable topological groupoid
Contents
Context
Higher geometry
Topology
topology (point-set topology , point-free topology )

see also differential topology , algebraic topology , functional analysis and topological homotopy theory

Introduction

Basic concepts

open subset , closed subset , neighbourhood

topological space , locale

base for the topology , neighbourhood base

finer/coarser topology

closure , interior , boundary

separation , sobriety

continuous function , homeomorphism

uniformly continuous function

embedding

open map , closed map

sequence , net , sub-net , filter

convergence

category Top

Universal constructions

Extra stuff, structure, properties

nice topological space

metric space , metric topology , metrisable space

Kolmogorov space , Hausdorff space , regular space , normal space

sober space

compact space , proper map

sequentially compact , countably compact , locally compact , sigma-compact , paracompact , countably paracompact , strongly compact

compactly generated space

second-countable space , first-countable space

contractible space , locally contractible space

connected space , locally connected space

simply-connected space , locally simply-connected space

cell complex , CW-complex

pointed space

topological vector space , Banach space , Hilbert space

topological group

topological vector bundle , topological K-theory

topological manifold

Examples

empty space , point space

discrete space , codiscrete space

Sierpinski space

order topology , specialization topology , Scott topology

Euclidean space

cylinder , cone

sphere , ball

circle , torus , annulus , Moebius strip

polytope , polyhedron

projective space (real , complex )

classifying space

configuration space

path , loop

mapping spaces : compact-open topology , topology of uniform convergence

Zariski topology

Cantor space , Mandelbrot space

Peano curve

line with two origins , long line , Sorgenfrey line

K-topology , Dowker space

Warsaw circle , Hawaiian earring space

Basic statements

Theorems

Analysis Theorems

topological homotopy theory

Contents
Definition
(AD-Renault 00 ) Recalled for instance in (Sims-Williams 12, p. 4 ).

(ANS 05, def. 1.3 )

Properties
Groupoid convolution algebra
(Tu 99, prop. 10.7 ), recalled as (Uuye 11, example 3.6 ).

This is due to (AD-Renault 00 ), recalled for instance as (ANS 05, prop. 1.9 )

References
Aidan Sims, Dana P. Williams, Amenability for Fell bundles over groupoids (arXiv:1201.0792 )
Johannes Aastrup, Ryszard Nest, Elmar Schrohe, A Continuous Field of C-algebras and the Tangent Groupoid for Manifolds with Boundary_ (arXiv:math/0507317 )
Jean-Louis Tu , La conjecture de Baum-Connes pour les feuilletages moyennables , K-Theory 17 (1999), no. 3, 215–264. MR 1703305 (2000g:19004) (Portico , subscription needed)
Last revised on August 15, 2013 at 02:05:35.
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