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Results tagged with fa.functional-analysis
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user 109527
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
4
votes
1
answer
1k
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Is the space of continuous functions from Polish space to Polish space Polish?
Theorem 4.19 in Kechris' Classical Descriptive Set Theory says that the space of continuous functions from a compact metric space to a Polish space is Polish. It is therefore obvious that the space of …
- 263
-1
votes
2
answers
390
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$X$ is Polish and $N$ is countable. Is $N^X$ Polish? [closed]
$X$ is a separable, completely metrizable topological space equipped with its sigma algebra of Borel sets. $N$ is a countable space.
$X^N$ is the collection of all mappings from $N$ to $X$. It is equi …
- 263
3
votes
0
answers
227
views
$f(x)>0$ and $f(y)>0$ implies $f(x+y)>0$, then there must exist an linear function $g$ such ...
Background: Let $x,y\in\mathbb (0,+\infty)^n$. $f$ is a continuous function on $\mathbb R^n_+=(0,+\infty)^n$. Consider the following condition (1), the sign of $f(x+y)$ is dependent on the sign of $f …
- 263
1
vote
0
answers
385
views
The perturbation of a convex function can also be convex?
$ W^{1,\infty}(D)\ni f:D\to\mathbb R, (x,y)\mapsto f(x,y)$, is a strictly increasing on both dimensions (i.e. if $x_1>x_2$ then $f(x_1,y)>f(x_2,y)$), lipschitz continuous function defined on a convex …
- 263