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Results tagged with metric-spaces
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user 43793
A metric space is a pair $(X,d)$, where $X$ is a set and $d:X \times X \to \mathbb{R}$ satisfies the following conditions for all $x,y,z \in X$. (Symmetry) $d(x,y)=d(y,x)$. (Identity of Indiscernibles) $d(x,y)=0$ if and only if $x=y$. (Triangle Inequality) $d(x,y)+d(y,z) \geq d(x,z)$.
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Locally compact space that is not topologically complete
A completely regular space is topologically complete, by definition, if it is complete for the finest uniformity compatible with the topology. Any locally compact space is clearly topologically compl …
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