The Alexandroff extension of a topological space X is Hausdorff if and only if X is Hausdorff and has this property. For 10 points each:
[10h] Name this topological property of groups that admit a notion of Fourier analysis.
ANSWER: local compactness [or locally compact; reject “compact”]
[10m] When X is not Hausdorff, the Alexandroff one-point compactification is less useful than a compactification denoted “beta X,” constructed by an American and this mathematician. This developer of a cohomology theory based on nerve complexes was the first to publish a proof of Tychonoff’s theorem.
ANSWER: Eduard Čech (“check”) [prompt on Stone–Čech compactification]
[10e] Čech cohomology is obtained via this relationship to Čech homology. Fourier analysis employs a “Pontryagin” form of this correspondence between two objects, which is used in graph theory to interchange vertices and faces.
ANSWER: duality [or word forms such as dualizing; accept Pontryagin duality]
<JC, Other Science (Math)>