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Let $X$ be a topological space. If there exists a simplicial complex $K$ and a homeomorphism $f:|K| \rightarrow X, X$ is said to be triangulable and the pair $(K, f)$ is called a triangulation of $X$.

Topology, Geometry and Physics- Nakhara, 2nd ed,pg-101

I have some doubts on the following definition:

  1. How does one actually 'think' of triangulating topological spaces? Is there some visual intuition for it?
  2. I am confused on how the homomorphism is done. I suppose it maybe mainly because I don't understand the topology of simplical complexes.
tryst with freedom
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    Have you tried triangulating, say the torus? This is usually one of the first examples you should encounter and almost any introductionary book should provide some figures (otherwise just search for the respective keywords in google). – Zest Jul 21 '22 at 16:16
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    The intuition is that you're representing the space as a bunch of triangles connected by their edges (or higher-dimensional simplexes connected by their faces), the way you'd triangulate a polygon. – Karl Jul 21 '22 at 16:20

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