"Dr. Chantal," wondered Bob, turning from the board for a moment, "could you use Brouwer’s theorem to show that if m doesn't equal n then M and N can't be homeomorphic?" Kate grinned. "Absolutely. Can anyone state Brouwer's theorem?"
When Kate had first appeared to teach the topology seminar, listed under Mielke's name, they had hovered uncomfortably in the hallway, waiting for the woman camped out in their seminar room to get herself sorted and leave. When she finally came out and inquired if there were waiting for Math 637, they wondered if she was the new departmental secretary, come to tell them that the class had moved.
She had introduced herself as Kathryn Chantal and explained that Prof. Mielke was serving as interim dean, but had asked her to fill in. As she began to write the syllabus on the board, Bob had leaned over to Mike and whisphered meant to be overheard, "How gullible does Mielke think we are? K. Chantal? As in Chantal's selection theorem? I've got half a mind to march down and call him on it." Mike elbowed him. "Wanna come?" Mike pointed.
Kate had given over the syllabus and begun writing a proof on the board. Given a sequence {Kn} of convex sets contained in a bounded set...
Fifteen minutes later, without saying a word, she had covered the board from top left to bottom right, finishing with one line: Therefore a metric space of convex bodies is locally compact. K. Chantal, Trans. Am. Math. Soc. 87, 369 (1953).
"My doctoral work. How gullible are you, Mr. Andrews?" Mike blushed and even Bob had the grace to look chagrined.
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