Urysohn space: Difference between revisions
(New page: ==Definition== A topological space <math>X</math> is termed a '''Urysohn space''' if given any two distinct points <math>x,y \in X</math>, there exists a continuous function <math>f:X \to...) |
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==Definition== | ==Definition== | ||
A topological space <math>X</math> is termed a '''Urysohn space''' if given any two distinct points <math>x,y \in X</math>, there exists a continuous function <math>f:X \to [0,1]</math> such that <math>f(x) = 0</math>, <math | A topological space <math>X</math> is termed a '''Urysohn space''' if given any two distinct points <math>x,y \in X</math>, there exists a continuous function <math>f:X \to [0,1]</math> such that <math>f(x) = 0</math>, <math>f(y) = 1</math>. | ||
==Facts== | ==Facts== | ||
Latest revision as of 01:42, 22 May 2026
Definition
A topological space is termed a Urysohn space if given any two distinct points , there exists a continuous function such that , .