Previous bonus - Next bonus

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

HeardPPBE %M %H %
7115.0780%56%14%

Back to bonuses

Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
CatholicNYU B0000
Columbia AVassar1001020ME
Columbia BJohns Hopkins A1010020MH
Maryland AColumbia C1001020ME
Maryland BJohn Jay001010E
Maryland CGeorgetown001010E
NYU AJohns Hopkins B1001020ME
SwarthmoreNYU C1001020ME

Summary

TournamentEditionMatchHeardPPBE %M %H %
California (North)Main Site✓326.67100%100%67%
CanadaMain Site✓1010.0060%30%10%
FloridaMain Site✓313.3367%67%0%
Great LakesMain Site✓510.0080%20%0%
MidwestMain Site✓816.2575%75%13%
NortheastMain Site✓516.0080%60%20%
OverflowMain Site✓412.50100%25%0%
South CentralMain Site✓210.0050%50%0%
SoutheastMain Site✓712.8686%29%14%
UKMain Site✓1220.0092%83%25%
Upper Mid-AtlanticMain Site✓815.0075%63%13%
Upstate NYMain Site✓417.50100%75%0%