Question
Answer the following about the intersection between algebraic topology and breakfast foods, for 10 points each.
[10e] A common joke holds that a coffee mug is the same as this surface since they are homeomorphic. Donuts and bagels are shaped like this surface.
ANSWER: torus [or tori; accept S-one cross S-one]
[10h] This type of map is often visualized as flattening a stack of pancakes, the union of which is the preimage of a neighborhood in the base. Up to equivalence, a simply connected space has only one of these maps.
ANSWER: covering maps [or covers; accept covering projections or covering spaces; accept universal covers]
[10m] The Borsuk–Ulam theorem gives an algebraic topology proof of the ham sandwich theorem, which concerns one of these subspaces that “cuts” n objects in half. These affine subspaces have dimension one less than the full space and generalize a two-dimensional analog.
ANSWER: hyperplanes [prompt on planes]
<TM, Other Science>
Summary
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