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Comb space : ウィキペディア英語版
Comb space
In mathematics, particularly topology, a comb space is a subspace of \R^2 that looks rather like a comb. The comb space has some rather interesting properties and provides interesting counterexamples. The topologist's sine curve has similar properties to the comb space. The deleted comb space is an important variation on the comb space.
==Formal definition==

Consider \R^2 with its standard topology and let ''K'' be the set \. The set ''C'' defined by:
:(\ \times () ) \cup (K \times ()) \cup (() \times \)
considered as a subspace of \R^2 equipped with the subspace topology is known as the comb space. The deleted comb space, D, is defined by:
:(\ \times \ ) \cup (K \times ()) \cup (() \times \) .
This is the comb space with the line segment \ \times (0,1) deleted.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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