Definition: (open cell). Let X be a Hausdorff space. A set c ⊂ X is an open(adsbygoogle = window.adsbygoogle || []).push({});

k − cell if it is homeomorphic to the interior of the open k-dimensional ball

D^{k}= {x ∈ R^{k}| x < 1}. The number k is unique by the invariance of

domain theorem, and is called dimension of c.

A 0-cell, 1-cell, 2-cell and 3-cell are called a vertex, edge, face and volume

respectively.

I am confused, what is the meaning of 0-cell and 1-cell. I can imagine a circle and a sphere without borders which resemble 2-cell and 3-cell. But how is vertex and lines are homeomorphic to D^{0}and D^{1}respectively. and how is the vertex is 0-cell and edge is 1-cell. I simply can not imagine that.

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# How is 0-cell is a vertex

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