Crap. I was gonna say "Guys. It's time for some sandwich theory."
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I was going to write a paper but life got in the way ;_;
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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
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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.
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This motivates considering a definition based on the subdivision of bread and subsets of the sandwich which reduce to trivial sandwiches via homomorphism
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This is why I introduced the "locally sandwich" criterion, which describes spaces that can be covered by/decomposed into sandwiches.
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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).
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My cat is being anxious. One sec.
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equivalent *to* presandwiches (which I think is a less awkward term than 'protosandwiches')
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What about deli meat on a sliced roll that has been almost, but not completely, cut in half (remaining "bread hinge" at one edge)?
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That's equivalent to a hot dog, which has already been discussed.
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Does this mean pita bread is unacceptable for a topological sandwich?
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If the bread is one continuous piece you have a proto- or presandwich, we've been discussing sandwich theory for weeks here
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"path" in this context means a curve (a continuous embedding of the unit interval) entirely contained in S.
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I am currently imagining sandwiches with infinitesimally small fillings.
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The unit ball requirement on B requires close inspection of the holes of each slice of bread
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Never mind, this has been discussed.
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.