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- W2795598045 abstract "We first show that in the function realizability topos every metric space is separable, and every object with decidable equality is countable. More generally, working with synthetic topology, every $T_0$-space is separable and every discrete space is countable. It follows that intuitionistic logic does not show the existence of a non-separable metric space, or an uncountable set with decidable equality, even if we assume principles that are validated by function realizability, such as Dependent and Function choice, Markov's principle, and Brouwer's continuity and fan principles." @default.
- W2795598045 created "2018-04-13" @default.
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- W2795598045 date "2018-04-02" @default.
- W2795598045 modified "2023-10-17" @default.
- W2795598045 title "Every metric space is separable in function realizability" @default.
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- W2795598045 doi "https://doi.org/10.23638/lmcs-15(2:14)2019" @default.
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