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Space Suggestion: Dijkstra's connected space #1843

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@Moniker1998

Space Suggestion

Let $X$ be the space $\gamma Y$ of the article An explosion point space without the fixed point property by Dijkstra.
The construction is too complicated to write here. Note that "totally disconnected" means "totally separated" for Dijkstra

Relationship to other spaces and properties

This space:
Has a dispersion point (in fact, explosion point)
Embeddable into Euclidean space (is one-dimensional so embeds into $\mathbb{R}^3$)
Does not have Fixed point property

This space is a counter-example to conjecture 1 in Dispersion Points and Fixed Points of Cobb and Voxman

Activity

  1. prabau commented on Sep 29, 2026

    @prabau
    Collaborator
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