Relating Bishopʼs function spaces to neighbourhood spaces

Annals of Pure and Applied Logic 164 (4):482-490 (2013)
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Abstract

We extend Bishopʼs concept of function spaces to the concept of pre-function spaces. We show that there is an adjunction between the category of neighbourhood spaces and the category of Φ-closed pre-function spaces. We also show that there is an adjunction between the category of uniform spaces and the category of Ψ-closed pre-function spaces

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10.1016/j.apal.2012.10.009

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Citations of this work

Sets Completely Separated by Functions in Bishop Set Theory.Iosif Petrakis - 2024 - Notre Dame Journal of Formal Logic 65 (2):151-180.

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References found in this work

Aspects of general topology in constructive set theory.Peter Aczel - 2006 - Annals of Pure and Applied Logic 137 (1-3):3-29.
Apartness spaces as a framework for constructive topology.Douglas Bridges & Luminiţa Vîţă - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.
Apartness spaces as a framework for constructive topology.Douglas Bridges & Luminia Vî - 2003 - Annals of Pure and Applied Logic 119 (1-3):61-83.

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