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In topology, a proximity space, also called a nearness space, is an axiomatization of notions of "nearness" that hold set-to-set, as opposed to the better known point-to-set notions that characterize topological spaces.
The concept was described by Frigyes Riesz (1909) but ignored at the time. It was rediscovered and axiomatized by V. A. Efremovič in 1934 under the name of infinitesimal space, but not published until 1951. In the interim, A. D. Wallace (1941) discovered a version of the same concept under the name of separation space.
Definition. A proximity space (X, δ) is a set X with a relation...
Let $T : [0, 1]\times [0, 1] \rightarrow [0, 1]$. A $t$-norm is a function $T$ with properties:
$1. T (x, 1) = x$
$2.$ If $y\leq z$ then $T(x,y)\leq T(x,z)$
$3. T (x, y) = T (y, x) $
$4. T (x, T (y, z)) = T (T (x, y), z) $
Prove $T(x,0)=0$.
I'm trying to prove $T(x,0)\geq 0$ and $T(x,0)\leq...9
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When there is only one question for the tag, it is showing as 1 questions.
It should be displayed as 1 question.
Given integer triangle $\triangle ABC$ such that $\dfrac{\sin B + n\sin C}{n \cos B + \cos C} = \sin A$ $(n \in \mathbb N)$. $M$ and $G$ are respectively the midpoint of $BC$ and the centroid of $\triangle ABC$. Prove that $[MBG] \in \mathbb N$.
We have that $[MBG] = \dfrac{[ABC]}{6}$, which...
