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The Ubiquitous Converse Lawvere Problem — AI Alignment Forum

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(This post was originally published on Oct 20th 2017, and is 1 of 4 posts brought forwarded today as part of the AI Alignment Forum launch sequence on fixed points.) In this post, I give a stronger version of the open question presented here, and give a motivation for this stronger property. This came out of conversations with Marcello, Sam, and Tsvi. Definition: A continuous function f : X → Y is called ubiquitous if for every continuous function g : X → Y , there exists a point x ∈ X such that f ( x ) = g ( x ) . Open Problem: Does there exist a topological space X with a ubiquitous function f : X → [ 0 , 1 ] X ? I will refer to the original problem as the Converse Lawvere Problem, and the new version as the the Ubiquitous Converse Lawvere Problem. I will refer to a space satisfying the conditions of (Ubiquitous) Converse Lawvere Problem, a (Ubiquitous) Converse Lawvere Space, abbreviated (U)CLS. Note that a UCLS is also a CLS, since a ubiquitous is always surjective, since

x The Ubiquitous Converse Lawvere Problem — AI Alignment Forum Fixed Points Decision theory Game Theory AI Frontpage 10 The Ubiquitous Converse Lawvere Problem by Scott Garrabrant 29th Nov 2018 3 min read 0 10 (This post was originally published on Oct 20th 2017, and is 1 of 4 posts brought forwarded today as part of the AI Alignment Forum launch sequence on fixed points.) In this post, I give a stronger version of the open question presented here , and give a motivation for this stronger property. This came out of conversations with Marcello, Sam, and Tsvi. Definition: A continuous function f

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