Packet C: Bonus 14
Spaces with this property are conceptually the topological analogue of a finite set in set theory. For 10 points each:
[10m] Name this ubiquitously discussed property in analysis and topology held by subsets of Rn (“R-N”) that are closed and bounded.
ANSWER: compactness [or compact spaces or compact sets]
[10h] This theorem states that an equicontinuous and bounded real-valued function on a compact set converges uniformly. It is often proven by taking a countable dense subset of a space, then using the Bolzano–Weierstrass theorem, then diagonalizing to construct a convergent subsequence.
ANSWER: Arzela–Ascoli theorem [or Ascoli–Arzela theorem]
[10e] Uniform convergence holds if the difference between terms becomes arbitrarily small for some N that depends only on a quantity denoted by this letter. Continuity and convergence are formalized by a definition named for this letter and delta.
ANSWER: epsilon [or epsilon–delta definition]
<UBC A, Other Science> | Packet C - Virginia Tech A, Waterloo A, UCSD A, UBC A
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 71 | 15.07 | 80% | 56% | 14% |
Conversion
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| California (North) | Main Site | ✓ | 3 | 26.67 | 100% | 100% | 67% |
| Canada | Main Site | ✓ | 10 | 10.00 | 60% | 30% | 10% |
| Florida | Main Site | ✓ | 3 | 13.33 | 67% | 67% | 0% |
| Great Lakes | Main Site | ✓ | 5 | 10.00 | 80% | 20% | 0% |
| Midwest | Main Site | ✓ | 8 | 16.25 | 75% | 75% | 13% |
| Northeast | Main Site | ✓ | 5 | 16.00 | 80% | 60% | 20% |
| Overflow | Main Site | ✓ | 4 | 12.50 | 100% | 25% | 0% |
| South Central | Main Site | ✓ | 2 | 10.00 | 50% | 50% | 0% |
| Southeast | Main Site | ✓ | 7 | 12.86 | 86% | 29% | 14% |
| UK | Main Site | ✓ | 12 | 20.00 | 92% | 83% | 25% |
| Upper Mid-Atlantic | Main Site | ✓ | 8 | 15.00 | 75% | 63% | 13% |
| Upstate NY | Main Site | ✓ | 4 | 17.50 | 100% | 75% | 0% |