Question
The metric that is equal to 1 if x is not equal to y, and equal to 0 if x is equal to y induces this topology. For 10 points each:
[10h] Identify this finest possible topology in which all subsets are open.
ANSWER: discrete topology
[10e] Any function from the discrete topology to another topological space always has this property because the pullback is always open. Functions with this property can be sketched without lifting the pencil from the paper.
ANSWER: continuity [or continuous functions]
[10m] The discrete topology has this property if it is finite. Topological spaces have this property if every open cover contains a finite subcover.
ANSWER: compactness
<Leo Law, Other Science>
Summary
| 2023 Penn Bowl @ Waterloo | 10/28/2023 | Y | 4 | 27.50 | 100% | 100% | 75% |
| 2023 Penn Bowl @ FSU | 10/28/2023 | Y | 2 | 15.00 | 100% | 50% | 0% |
| 2023 Penn Bowl (Harvard) | 10/21/2023 | Y | 3 | 20.00 | 100% | 67% | 33% |
| 2023 Penn Bowl (Mainsite) | 10/21/2023 | Y | 6 | 21.67 | 100% | 67% | 50% |
| 2023 Penn Bowl (Norcal) | 10/28/2023 | Y | 2 | 20.00 | 100% | 100% | 0% |
| 2023 Penn Bowl (South Central) | 10/28/2023 | Y | 3 | 20.00 | 100% | 67% | 33% |
| 2023 Penn Bowl (UK) | 10/28/2023 | Y | 5 | 24.00 | 100% | 100% | 40% |
| 2023 Penn Bowl @ UNC | 10/28/2023 | Y | 4 | 22.50 | 100% | 75% | 50% |
Data
| Berkeley A | Berkeley C | 0 | 10 | 10 | 20 |
| Stanford | Berkeley B | 0 | 10 | 10 | 20 |