Bishop's notion of a function space, here called a Bishop space, is a constructive function-theoretic analogue to the classical set-theoretic notion of a topological space. Here we introduce the quotient, the pointwise exponential and the completely regular Bishop spaces. For the latter we present results which show their correspondence to the completely regular topological spaces, including a generalized version of the Tychonoff embedding theorem for Bishop spaces. All our proofs are within Bishop's informal system of constructive mathematics BISH.
Completely Regular Bishop Spaces
Petrakis, Iosif
2015-01-01
Abstract
Bishop's notion of a function space, here called a Bishop space, is a constructive function-theoretic analogue to the classical set-theoretic notion of a topological space. Here we introduce the quotient, the pointwise exponential and the completely regular Bishop spaces. For the latter we present results which show their correspondence to the completely regular topological spaces, including a generalized version of the Tychonoff embedding theorem for Bishop spaces. All our proofs are within Bishop's informal system of constructive mathematics BISH.
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