There are only few questions in those tags at the moment. (Of course, the number of questions is not the main criterion by which the appropriateness of a tag should be judged.)
Let $f:\mathbb R^2 \to \mathbb R$ be a function such that $|f(x)-f(y)|\ge 3\|x-y\| , \forall x,y \in \mathbb R^2$ , then is it true that $f$ maps open sets of $\mathbb R^2$ to open sets of $\mathbb R$ ? I can show that $f$ maps open sets to open sets in $f(\mathbb R^2)$ , so to prove the claim we...
Let X,Y be topological spaces.
Prove the following statements are equivalent.
(The question is attached by image file.)
http://i.stack.imgur.com/PrWw4.png
I completely proved (1) -> (2)
But couldn't find any idea to solve (2) ->(3) and (3) ->(1).
[Trying to solve using cl(B)=int(B)-b(B), ...
Let $X,Y$ be metric spaces , $f:X \to Y$ be a continuous and closed map , then is it true that the boundary of $f^{-1}(\{y\})$ is compact for every $y \in Y$ ?
With just three questions in both, I'm not sure if anyone can actually have grounds to protest. I just don't know if "open map" is something that will be hard to search for.
You know, hard enough, that it needs a separate tag.
@AsafKaragila Well it can be called open map or open function. If you want also catch formulations of the form "Show that this map is open" you cannot search for the exact phrase "open map". But searching for open map or open function will very probably catch many posts where some function and some open set are mentioned.
A moderator will be needed to approve those synonyms - there will be very few people with score 5 or higher in a relatively new tag with a few questions.
I'm not sure where to ask this, but I just saw this question. math.stackexchange.com/questions/1832178/… I'm sure the current tag isn't very helpful, but I'm not sure either which tags it should have. Any suggestions?
I was recently wondering if there is some quicker way to compute ${x_1}^k+{x_2}^k+\dots+{x_n}^k$ for any natural $k$ than just exponentiation and adding one-by-one? Thanks in advance.
I was recently wondering if there is some quicker way to compute ${x_1}^k+{x_2}^k+\dots+{x_n}^k$ for any natural $k$ than just exponentiation and adding one-by-one? Thanks in advance.
