Question
To explain sets with this property, James Munkres argued “topological sets are not like a door.” For 10 points each:
[10m] Identify this property exhibited by the empty set and the entire set in any topology. In the discrete topology, every set has this property.
ANSWER: clopen [accept closed-open set accept any description mentioning the set is both closed and open; prompt on closed or open alone]
[10e] With the union and intersection, the clopen subsets of a topological space form an algebraic structure named for this person. Logical operators like “AND” and “OR” are used in a branch of algebra named for this English mathematician.
ANSWER: George Boole [accept Boolean algebras; accept Boolean lattices]
[10h] A representation theorem named for this mathematician states that every Boolean algebra is isomorphic to the set of clopen subsets of some topological space. With a Czech mathematician, this man names a method for generating the largest compact space containing a given topological space.
ANSWER: Marshall Harvey Stone (The results mentioned are the Stone representation theorem of Boolean algebras and the Stone-Čech compactification.)
<Science - Other Science - Math>
Summary
| 2024 ARGOS @ Brandeis | 03/22/2025 | Y | 3 | 16.67 | 100% | 33% | 33% |
| 2024 ARGOS @ Chicago | 11/23/2024 | Y | 6 | 16.67 | 100% | 50% | 17% |
| 2024 ARGOS @ Christ's College | 12/14/2024 | Y | 3 | 16.67 | 100% | 33% | 33% |
| 2024 ARGOS @ Columbia | 11/23/2024 | Y | 3 | 6.67 | 67% | 0% | 0% |
| 2024 ARGOS @ Stanford | 02/22/2025 | Y | 3 | 20.00 | 100% | 67% | 33% |
| 2024 ARGOS Online | 03/22/2025 | Y | 3 | 20.00 | 100% | 67% | 33% |
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