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Date: 24-5-2021
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Definition A simplicial map ϕ: K → L between simplicial complexes K and L is a function ϕ: Vert K → Vert L from the vertex set of K to that of L such that ϕ(v0), ϕ(v1), . . . , ϕ(vq) span a simplex belonging to L whenever v0, v1, . . . , vq span a simplex of K.
Note that a simplicial map ϕ: K → L between simplicial complexes K and L can be regarded as a function from K to L: this function sends a simplex σ of K with vertices v0, v1, . . . , vq to the simplex ϕ(σ) of L spanned by the vertices ϕ(v0), ϕ(v1), . . . , ϕ(vq).
A simplicial map ϕ: K → L also induces in a natural fashion a continuous map ϕ: |K| → |L| between the polyhedra of K and L, where
whenever 0 ≤ tj ≤ 1 for j = 0, 1, . . . , q,
simplex of K. The continuity of this map follows immediately from a straight forward application of Lemma 5.2. Note that the interior of a simplex σ of K is mapped into the interior of the simplex ϕ(σ) of L.
There are thus three equivalent ways of describing a simplicial map: as a function between the vertex sets of two simplicial complexes, as a function from one simplicial complex to another, and as a continuous map between the polyhedra of two simplicial complexes. In what follows, we shall describe a simplicial map using the representation that is most appropriate in the given context.
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دراسة يابانية لتقليل مخاطر أمراض المواليد منخفضي الوزن
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اكتشاف أكبر مرجان في العالم قبالة سواحل جزر سليمان
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المجمع العلمي ينظّم ندوة حوارية حول مفهوم العولمة الرقمية في بابل
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