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Results tagged with fa.functional-analysis
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user 18263
Banach spaces, function spaces, real functions, integral transforms, theory of distributions, measure theory.
47
votes
6
answers
5k
views
Can we actually find any fixed points with Brouwer's theorem?
Background
At the risk of greatly oversimplifying matters, let me state a heuristic from Granas and Dugundji's beautiful book: fixed point theorems fall into two broad categories. The first class is …
- 15.5k
8
votes
3
answers
481
views
Does the metric space of compact metric spaces satisfy the binary intersection property?
A metric space $Y$ has the binary intersection property provided that whenever a collection of closed balls in $Y$ intersects pairwise, then there is a common intersection point.
Does the metric s …
- 15.5k
7
votes
Between Tietze's and Dugundji's extension theorems
Bad News
The answer to Q3 as stated is no. Let $X$ be the Michael line, and let $Y$ be the closed subset consisting of all the rationals. Then, there is no bounded linear extension $C(Y,\mathbb{R}) \t …
- 15.5k
3
votes
Accepted
A Fixed point Theorem that does not need the convexity of set valued map?
In the absence of convex images, one typically relies on algebraic topology as you have guessed. If your set-valued map has a reasonably nice domain and contractible images, then you can easily string …
- 15.5k
2
votes
Representation of Banach spaces partially ordered by solid, normal, minihedral cones
Most of the proofs of this result are stated in terms of Banach lattices rather than in terms of solid, normal and minihedral cones; this might explain why Google searches are being unfriendly.
In an …
- 15.5k