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1. Let (X, d) be a locally compact separable metric space. Show that its one-point compactification is metrizable.
2. Let X be any noncompact metric space, considered as a subset of its Tychonoff-C? ech compactification K . Let y ∈ K \X . Show that K is not metrizable by showing that there is no sequence xn ∈ X with xn → y in K . Hint: If xn → y, by taking a subsequence, assume that the points xn are all different. Then, {x2n }n≥1 and {x2n-1}n≥1 form two disjoint closed sets in X . Apply Urysohn's Lemma (2.6.3) to get a continuous function f on X with f (x2n ) = 1 and f (x2n-1) = 0 for all n. So {xn } cannot converge in K to y.
eu european union countries report that 46 of their labor force is female. the united nations wants to determine if the
the following are the hours of operation to failure of 38 light bulbs.150 389 345 310 20 310 175 376 334 340 332 331
Create a 98 percent confidence interval for the population mean.
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black hair in the guinea pig is dominant to white hair in families of 5 offsprings where both parents are heterozygous
please respond with your thoughtsopinions and use examples to support your answer on the two separate posts in at least
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