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Definition 0.1 $C_c(\mathsf{G})$ is defined as the class of continuous functions acting on a topological groupoid $\mathsf{G}$ with compact support, and with values in a normed space, field,, or algebraic structure. In most applications it will, however, suffice to select $\mathsf{G}$ as a locally compact (topological) groupoid, $\mathsf{G}_{lc}$ , support for this space of continuous functions.

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Other names:

space of continuous functions with compact support on a topological groupoid

Also defines:

space of continuous functions with compact support on a topological groupoid

Keywords:

continuous function space, locally compact groupoids, space of continuous functions with compact support on a topological groupoid

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, born on 2008-07-26, modified 2008-09-15.
Object id is 10877, canonical name is C_cG.
Accessed 472 times total.

Classification:

AMS MSC:	22D05 (Topological groups, Lie groups :: Locally compact groups and their algebras :: General properties and structure of locally compact groups)
	26B05 (Real functions :: Functions of several variables :: Continuity and differentiation questions)
	26A15 (Real functions :: Functions of one variable :: Continuity and related questions )
	54C05 (General topology :: Maps and general types of spaces defined by maps :: Continuous maps)
	55U40 (Algebraic topology :: Applied homological algebra and category theory :: Topological categories, foundations of homotopy theory)
	55P10 (Algebraic topology :: Homotopy theory :: Homotopy equivalences)
	55N20 (Algebraic topology :: Homology and cohomology theories :: Generalized homology and cohomology theories)
	55N33 (Algebraic topology :: Homology and cohomology theories :: Intersection homology and cohomology)

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