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Results tagged with gn.general-topology
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user 9652
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
4
votes
Continuity of $\arg\min$
The answer is no (also for the question with $\epsilon$).
Here is a counterexample:
Consider $m=n=1$ and
$$
f(x,y) = (x^2-1)^2 + yx.
$$
For $y>0$ there is a unique minimizer to $\min_x f(x,y)$ whi …
- 12.7k
3
votes
Generalized Stokes' theorem
As said in the article, you find these results in book on geometric measure theory. Maybe "Geometric Integration Theory" by Krantz and Parks can be of help. Theorem 6.2.12 (not in the preview on Googl …
- 12.7k
18
votes
Notions of convergence not corresponding to topologies
Since that question popped up on the screen again I add something to the list (although I am pretty late to the party): The fact that pointwise almost everywhere convergence is not topological is nice …
- 12.7k
19
votes
4
answers
8k
views
Unique limits of sequences plus what implies Hausdorff?
It is known that there are non-Hausdorff spaces which admit unique limits for all convergent sequence (see here) and it is also known that unique limits for nets implies Hausdorff.
What I am wonderin …
- 12.7k
4
votes
How does the parity of $n$ affect the properties of $\mathbb{R}^n$?
The hairy ball theorem states that there is no nonvanishing continuous tangent vector field on even-dimensional spheres.
6
votes
Accepted
Fréchet L-Spaces
I think that these spaces don't go under the name of $L$ spaces anymore. Actually, I am not sure if there is a consensus on how these structures are called today.
A good place to start is the fairly r …
- 12.7k
11
votes
Is the boundary $\partial S$ analogous to a derivative?
Another, not too mathematical, analogy comes from image processing. There you can consider an image $u$ as a real valued function on a rectangle, say. A basic method for edge detection is to calculate …
- 12.7k