Continuous functions with compact support

Sudip Kumar Acharyya, K.C. Chattopadhyaya, Partha Pratim Ghosh


The main aim of this paper is to investigate a subring of the ring of continuous functions on a topological space X with values in a linearly ordered field F equipped with its order topology, namely the ring of continuous functions with compact support. Unless X is compact, these rings are commutative rings without unity. However, unlike many other commutative rings without unity, these rings turn out to have some nice properties, essentially in determining the property of X being locally compact non-compact or the property of X being nowhere locally compact. Also, one can associate with these rings a topological space resembling the structure space of a commutative ring with unity, such that the classical Banach Stone Theorem can be generalized to the case when the range field is that of the reals.


Ordered Fields; Zero Dimensional Spaces; Strongly Zero Dimensional Spaces; Compactifications

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1. Finite frames, P-frames and basically disconnected frames
Sudip Kumar Acharyya, Goutam Bhunia, Partha Pratim Ghosh
Algebra universalis  vol: 72  issue: 3  first page: 209  year: 2014  
doi: 10.1007/s00012-014-0296-x

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