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Results tagged with continuity
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user 8628
11
votes
Accepted
Topological conditions forcing continuity
It's possible to find a sufficient condition without putting any restraint on the spaces $X$ or $Y$.
Let $Z$ be the Sierpinski space, that is $Z$ has $\{0,1\}$ as a base set, and $\tau = \{\emptyset, …
- 48.9k
-2
votes
1
answer
472
views
Injective uniformly continuous function $f:\mathbb{Z}\times \mathbb{Z}\to \mathbb{Z}$? [closed]
We say that a function $f: \mathbb{Z}\times \mathbb{Z}\to \mathbb{Z}$ is uniformly continuous if there is an integer $K\geq 1$ such that
whenever $(x,y),(x',y')\in \mathbb{Z}\times \mathbb{Z}$ with $ …
- 48.9k
5
votes
1
answer
225
views
"Uniformly continuous" environment sum of a bijection $\varphi:\mathbb{Z}\times \mathbb{Z} \...
Given any function $f: \mathbb{Z}\times \mathbb{Z}\to \mathbb{Z}$ we define the environment sum of $(x,y)\in\mathbb{Z}\times \mathbb{Z}$ with respect to $f$ by
$$\text{es}_f(x,y) = \sum\{f(x', y'): |( …
- 48.9k