Point (geometry)
Topological dimension

The topological dimension of a topological space X {\displaystyle X} is defined to be the minimum value of n, such that every finite open cover A {\displaystyle {\mathcal {A}}} of X {\displaystyle X} admits a finite open cover B {\displaystyle {\mathcal {B}}} of X {\displaystyle X} which refines A {\displaystyle {\mathcal {A}}} in which no point is included in more than n +1 elements. If no such minimal n exists, the space is said to be of infinite covering dimension.

A point is zero-dimensional with respect to the covering dimension because every open cover of the space has a refinement consisting of a single open set.
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