A tale of three hedgehogs

Bachelor thesis, Preprint English OPEN
Torres, Igor Arrieta;
  • Subject: general topology | Mathematics - General Topology | metric hedgehog | collectionwise normal | quotient hedgehog | topology | collectionwise normality | compact hedgehog | metric spaces | discrete family | hedgehogs | Kowalsky’s Hedgehog Theorem

[EN] In this work we study three topologies defined over the same set: the hedgehog. As the name suggests, the hedgehog can be described as a set of spines identified at a single point. The first topology on the hedgehog will be a quotient topology, and the resulting sp... View more
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    k k two cases. First, if x < Sn=1 Fn, by finiteness U = X r Sn=1 Fn is an open neighborhood of x and clearly it does not intersect any of the F1, . . . , Fk.

    Assume now that x ∈ Fn0 for an n0 ∈ {1, . . . k}. Let U = X r Sn,n0 Fn. Since F1, . . . , Fk are pairwise disjoint, we have x ∈ U. By finiteness, U is open, and thus U is an open neighborhood of x. Finally, by construction, U only intersects Fn0. Hence, the discreteness condition is verified. 2 max{|t − t0|, |s − s0|} <

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