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In topology and related branches of mathematics, a T1 space is a topological space in which, for every pair of distinct points, each has a neighborhood not containing the other. An R0 space is one in which this holds for every pair of topologically distinguishable points. The properties T1 and R0 are examples of separation axioms. ==Definitions== Let ''X'' be a topological space and let ''x'' and ''y'' be points in ''X''. We say that ''x'' and ''y'' can be ''separated'' if each lies in a neighborhood which does not contain the other point. *''X'' is a T1 space if any two distinct points in ''X'' are separated. *''X'' is an R0 space if any two topologically distinguishable points in ''X'' are separated. A T1 space is also called an accessible space or a Fréchet space and a R0 space is also called a symmetric space. (The term ''Fréchet space'' also has an entirely different meaning in functional analysis. For this reason, the term ''T1 space'' is preferred. There is also a notion of a Fréchet-Urysohn space as a type of sequential space. The term ''symmetric space'' has another meaning.) 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「T1 space」の詳細全文を読む スポンサード リンク
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