We need a formal standard definition of a topological sandwich. First attempt: A topological sandwich is a topological space S = B ∪ M ∪ B', such that: 1) Each of B, M, B' is homeomorphic to the unit ball, 2) Every path from a point of B to a point of B' intersects M.
-
Show this thread
-
Replying to @St_Rev
I was going to write a paper but life got in the way ;_;
1 reply 0 retweets 0 likes -
Replying to @0xdeadbabe @St_Rev
Anyway, my definition is a bit looser than yours, as it drops the unit ball homeomorphism requirement, given the bagelwich case, which is CLEARLY a sandwich
2 replies 0 retweets 1 like -
Replying to @0xdeadbabe @St_Rev
But the Swiss cheese sandwich case is interesting; also consider the case where you have one large section of filling sandwiched between four pieces of bread.
1 reply 0 retweets 0 likes -
Replying to @0xdeadbabe @St_Rev
This motivates considering a definition based on the subdivision of bread and subsets of the sandwich which reduce to trivial sandwiches via homomorphism
2 replies 0 retweets 1 like -
Replying to @0xdeadbabe
This is why I introduced the "locally sandwich" criterion, which describes spaces that can be covered by/decomposed into sandwiches.
2 replies 2 retweets 7 likes -
Replying to @St_Rev @0xdeadbabe
If one uses my minimal definition of sandwich, then I conjecture that generalized sandwiches (spaces constructed by surgery on minimal sandwiches) are equivalent presandwiches (spaces meeting the locally sandwich criterion).
1 reply 0 retweets 5 likes -
-
Replying to @0xdeadbabe
equivalent *to* presandwiches (which I think is a less awkward term than 'protosandwiches')
1 reply 0 retweets 1 like -
Replying to @St_Rev
If I understand this correctly, presandwiches are decomposable into disjoint sets, one which is minimally sandwich in every nhood and one which is only presandwich in every nhood?
1 reply 0 retweets 1 like
A space P = B ∪ M ∪ B' is locally sandwich if: Every point p in P has an open neighborhood S_p, such that: S_p = (S_p ∩ B) ∪ (S_p ∩ M) ∪ (S_p ∩ B') is a (minimal) sandwich.
-
-
Replying to @St_Rev
This seems like an accurate definition, off the top of my head.
0 replies 0 retweets 0 likesThanks. Twitter will use this to make your timeline better. UndoUndo
-
Loading seems to be taking a while.
Twitter may be over capacity or experiencing a momentary hiccup. Try again or visit Twitter Status for more information.
. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.