Steven Krantz remarked that it was once said that “anyone who could survive a year of” a topology-infused book by this author “was a real mathematician.” For 10 points each:
[10h] What mathematician’s notoriously concise textbook Principles of Mathematical Analysis is sometimes nicknamed for him and the word “baby”?
ANSWER: Walter Rudin [accept “Baby Rudin”]
[10e] In the textbook’s proofs, Rudin sometimes neglects the case of the metric space over this set. Only one possible topology can be defined on this set, which is denoted by an “O” with a slash through it.
ANSWER: empty set [accept empty space; accept null set]
[10m] Walter Rudin’s wife Mary Ellen Rudin gave a short proof that all metric spaces have the “para-” variant of this property. Procedures named for imparting this property include ones called “Stone–Čech” (“stone check”) and “one-point.”
ANSWER: compact space [or compactness; accept compactification or Stone–Čech compactification or one-point compactification; accept paracompact space or paracompactness]
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