High Quality Content by WIKIPEDIA articles! In topology and related branches of mathematics, T1 spaces and R0 spaces are particular kinds of topological spaces. The T1 and R0 properties are examples of separation axioms. A T1 space is also called an accessible space or a Frechet space and a R0 space is also called a symmetric space. (The term Frechet 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 Frechet-Urysohn space as a type of sequential space. The term symmetric space has another meaning.) 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 an open set which does not contain the other point. * X is a T1 space if any two distinct points in X can be separated. * X is a R0 space if any two topologically distinguishable points in X can be separated.

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