Talk:Schauder fixed-point theorem: Difference between revisions

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Undid revision 1285925273 by Logicdavid (talk)
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Since x is a fixed point of T in K if and only if x is a fixed point in T(K), this theorem still uses the compactness of the set.
--[[User:Chyyr|Chyyr]] ([[User talk:Chyyr|talk]]) 08:27, 3 December 2020 (UTC)
 
== References missing in text ==
 
The article states ``[Schauder's Fixed Point Theorem] asserts that if is a nonempty convex closed subset of a Hausdorff topological vector space and is a continuous mapping of into itself such that is contained in a compact subset of , then has a fixed point. That's not what is called Schauder's Fixed Point Theorem in most texts in the literature, namely because the latter usually concern Banach spaces. The theorem as stated here is moreover without citation. This is a significant problem, in my view. Where is this purported theorem from, exactly? Logicdavid (talk) 16:34, 16 April 2025 (UTC) [[User:Logicdavid|Logicdavid]] ([[User talk:Logicdavid|talk]]) 16:36, 16 April 2025 (UTC)