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1986•Proceedings of the American Mathematical SocietyRequires access

Note on Compact Sets of First Baire Class Functions

Roman Pol

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Abstract

We give an example of a separable compact subspace of the space of first Baire class functions on the irrationals which cannot be embedded in the space of first Baire class functions on the Cantor set, both of the function spaces being considered with the pointwise topology. This answers a question asked in [Ta, Problem 14-2-4].

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What this paper is about

We give an example of a separable compact subspace of the space of first Baire class functions on the irrationals which cannot be embedded in the space of first Baire class functions on the Cantor set, both of the function spaces being considered with the pointwise topology. This answers a question asked in [Ta, Problem 14-2-4].

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OpenAlex reports 3 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We give an example of a separable compact subspace of the space of first Baire class functions on the irrationals which cannot be embedded in the space of first Baire class functions on the Cantor set, both of the function spaces being considered with the pointwise topology. This answers a question asked in [Ta, Problem 14-2-4].

Key concepts: Baire category theorem, Baire measure, Baire space, Mathematics, Class (philosophy), Subspace topology, Pointwise, Separable space

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