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Results tagged with metric-spaces
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user 53155
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) $d(x,y)+d(y,z) \geq d(x,z)$.
14
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Does existence of midpoints imply intrinsic?
It is well-known, that a complete metric space, where any two points have a midpoints ($\forall x,y~ \exists z:~d(x,z)=d(y,z)=\frac{d(x,y)}{2}$) is strictly intrinsic, in the sense that any $x,y$ can …
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Space of curves
I am reading Burago, Burago & Ivanov's book where they distinguish the notion of a curve and a path in the following way:
a path in a topological space $X$ is simply a (continuous) map from a connecte …
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2
votes
1
answer
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Is any submetrizable linear topology linearly submetrizable?
Let $E$ be a vector space. A topology $\tau$ on $E$ is called (linearly) submetrizable if there is a (linear) metrizable topology $\pi$ on $E$ which is weaker than $\tau$, i.e. $\pi\subset\tau$.
Is i …
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