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 one of these algebraic structures named for an English mathematician. Operations on these structures include “AND” and “OR.”
ANSWER: 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 H(arvey) Stone [accept Stone representation theorem; accept Stone-Čech compactification]
<Science - Other Science - Math>
Summary
| 2024 ARGOS @ McMaster | 11/17/2024 | Y | 5 | 24.00 | 80% | 100% | 60% |
Data
| I'd prefer to have the team name be Christensen et al. than anything that Erik cooks up | Moderator Can't Neg me While in Alpha | 10 | 10 | 10 | 30 |
| Communism is Soviet power plus the yassification of the whole country | Ryan Wesley Routh's 10 000 NATO-trained Afghan Quizbowlers | 10 | 10 | 0 | 20 |
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| Simpson Agonistes: The Crisis of Donut | Tensei Shitara Flashcard Data Ken | 10 | 0 | 10 | 20 |
| The Only Existing Manuscript from A Clockwork Orange | as rational as the square root of two power bottoms | 10 | 10 | 10 | 30 |