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In mathematics, particularly topology, a comb space is a subspace of
Contents
Formal definition
Consider
considered as a subspace of
This is the comb space with the line segment
Topological properties
The comb space and the deleted comb space have some interesting topological properties mostly related to the notion of connectedness.
1. The comb space is an example of a path connected space which is not locally path connected.
2. The deleted comb space, D, is connected:
3. The deleted comb space is not path connected since there is no path from (0,1) to (0,0):