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Additional resources for American Mathematical Monthly, volume 107, number 7, August-September 2000

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We argue, however, that this important new freedom should not be mistaken for independence from mathematics. 3. STATISTICS IS, ALAS, DIFFERENT. Should statisticians gloat? Not at all. Each of the strengths we have noted has a darker side. The picture that emerges when all the pieces come together is one of organizational weakness. The advantages of statistics over mathematics in our current environment are cultural, and cultural strength rarely outweighs organizational weakness. God is on the side of the big battalions.

X n) is compact}. ", JiI = {A: 3 k E Z+ such that A c n~1 Bf. (x n), where rn E Tn for n :::; k) . It is now clear that JiI has a countable cofinal subset and is thus a metric bomology, which means that there is an admissible metric d for X whose closed balls are all compact, a fact first observed by H. Vaughn [4]. Conversely, local compactness and separability of the space are forced by the compactness of closed balls (a sigma compact metrizable space is separable [5, p. 126]). We indicate a proof of the nontrivial part of Theorem A that relies on Hu's theorem.

Then X rt. JiI, and by local compactness alone, the closure of each A E JiI has a compact neighborhood. For the remaining condition, let p be an admissible metric for X, and let {x n : n E Z+} be a countable dense subset of X. '(x n) is compact}. ", JiI = {A: 3 k E Z+ such that A c n~1 Bf. (x n), where rn E Tn for n :::; k) . It is now clear that JiI has a countable cofinal subset and is thus a metric bomology, which means that there is an admissible metric d for X whose closed balls are all compact, a fact first observed by H.

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American Mathematical Monthly, volume 107, number 7, by The Mathematical Association of America
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