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1. • CommentRowNumber1.
   • CommentAuthornLab edit announcer
   • CommentTimeApr 14th 2025
   • PermaLink
   Author: nLab edit announcer
   Format: MarkdownItexStarting page on the "principle of enough functions": the formal [[locale]] of the [[function space]] $\mathbb{R}^\mathbb{R}$ of [[continuous]] [[Dedekind real number|real]] [[endofunctions]] is a [[spatial locale]], as described in * {#Moerdijk84} [[Ieke Moerdijk]], *Heine-Borel Does Not Imply the Fan Theorem*, Journal of Symbolic Logic, vol. 49, no. 2, 1984, pp. 514–519. ([doi:10.2307/2274182](https://doi.org/10.2307/2274182)) Anonymouse <a href="https://ncatlab.org/nlab/revision/principle+of+enough+functions/1">v1</a>, <a href="https://ncatlab.org/nlab/show/principle+of+enough+functions">current</a>

   Starting page on the “principle of enough functions”: the formal locale of the function space of continuous real endofunctions is a spatial locale, as described in

   • {#Moerdijk84} Ieke Moerdijk, Heine-Borel Does Not Imply the Fan Theorem, Journal of Symbolic Logic, vol. 49, no. 2, 1984, pp. 514–519. (doi:10.2307/2274182)

   Anonymouse

   v1, current