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Results tagged with gn.general-topology
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user 37822
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
11
votes
Accepted
If a subspace $F$ is contained in a subspace $G$, and $H$ is close to $G$, can we choose a s...
The answer is "No". You can derive this from Lemma 5.9 and Proposition 5.3 in my paper Ostrovskiĭ, M. I. Topologies on the set of all subspaces of a Banach space and related questions of Banach space …
- 12.9k
4
votes
Accepted
The anti-symmetric property of the collection of all compact convex sets of a Banach space
If I understand you correctly, the question is answered in the book Bessaga-Pelczynski, "Selected topics in infinite-dimensional topology", Warsaw, 1975. Combine Theorem 3.1 and Proposition 3.1 in tha …
- 4,878
2
votes
A question about subsets of plane
In order to prove that $X$ cannot exist, I think that you can argue in the following way: for $x$ to satisfy this condition in $X$, the set $X$ should contain a straight or a zig-zag "discrete ray" wi …
- 4,878
4
votes
Term for a metric space for which the triangle inequality is strict?
The only thing which I recall in this connection is: Blumenthal in his "Theory and Applications of Distance Geometry" (page 56) calls three points a linear triple if the triple is congruent with a tri …
- 4,878