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I'd be happier with a clearer introducing paragraph. In particular it seems to contradict the precise definition given after. There is an ambiguity as to whether or not the balls are closed. There seems to be a typo with a union symbol followed by deg. Btw the mainstream definition of a ball without
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specification of "open" or "closed" is the open version. Also, examples (and counterexamples) would be welcome (besides the dogbone example, which concerns not the definition in itself but a consequence thereof).
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