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Results tagged with metric-spaces
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user 16537
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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Turning an integer-valued semimetric into a smaller pseudometric by preserving the kernel an...
Let $X$ be a set, and let $\mathfrak d$ be a semimetric on $X$, namely, a non-negative function $X \times X \to \mathbf R$ such that $\mathfrak d(x,x) = 0$ and $\mathfrak d(x,y) = \mathfrak d(y,x)$ fo …
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If $(\mathbb M, \tau)$ is a topological monoid, is $\tau$ always induced by a [left] subinva...
Let me start by recalling some basic definitions (just for the sake of avoiding misunderstandings due to the vocabulary of the post).
Basically following some ideas of W. Lawvere (but not his termino …
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If $(\mathbb M, \tau)$ is a topological monoid, is $\tau$ always induced by a [left] subinva...
I apologize for answering my own question.
Let $\mathcal K = (\mathbb K, \tau)$ be a T1 topological unital ring, with $\mathbb K = (K, +, \cdot)$, and let $\mathbb K_{(\cdot)}$ be the multiplicative …
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First-countable topological monoids without local absorbing elements whose topology is induc...
This is a follow up of Question 163246. For the reader's convenience, let me first copy&paste some basic definitions.
We let a semimetric on a set $X$ be a function $d: X \times X \to [0,\infty]$ suc …
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