Glue, paper, and scissors ready. You make one of these surfaces by cutting out a strip of paper, giving it a half-twist, and gluing its ends together. For 10 points each:
[10e] Name these non-orientable one-sided surfaces, two of which can be theoretically “glued” together to make a Klein bottle.
ANSWER: Möbius strip [or Möbius band or Möbius loop]
[10m] You glue together two manifolds by their cobordism, a manifold for which this set is the disjoint union of the two manifolds. By definition, a closed set contains its corresponding set of this type.
ANSWER: boundary set [or boundaries; accept set of boundary points] (The root of “cobordism” is “bord,” the French word for “boundary.”)
[10h] Your cobordism has this property that the Heine–Borel theorem equates with closure and boundedness in R·n. Every open cover of a space with this property admits a finite subcover.
ANSWER: compactness [accept topological compactness]
<Steven Yuan, Science - Math> ~20455~ <Editor: David Bass>