For questions about separable spaces, i.e., topological spaces containing a countable dense set.
A separable space is a topological space which contains a countable dense set.
Questions tagged [separable-spaces]
504 questions
0
votes
0 answers
A question of countable product and uncountable product
It is intuitive and easy to show that a countable product of separable spaces is separable. It is tempting to think that an uncountable product of separable spaces will not be separable
(a) Show that R^R is separable. Can the same be said about…
0
votes
1 answer
sum of separable norms is separable
Let $X$ be a linear space and let $\|.\|_1$, $\|.\|_2$ be two norms on $X$ such that $X_i:=(X,\|.\|_i)$ is separable for $i=1,2$. Then also $Y:=(X,\|.\|_1+\|.\|_2)$ is separable.
I tried the following: we know that then $X_1\times X_2$ equipped with…
elliptic
- 376