# Real Analysis Questions and answers

Topics

51). $$Z^{+} \times Z^{+}$$ is
 A). countable B). uncountable C). bounded D). none of these
52). Every open covering of a set A has a finite I subcovering if A is
 A). closed and bounded B). closed only C). bounded only D). none of these
53). Uniform continuity implies continuity, The converse is true if it is
 A). covering B). connected C). compact D). none of these
54). The set Q is a
 A). countable set B). uncountable set C). bounded set D). none of these
55). Every subset of a countable sets is
 A). countable B). uncountable C). bonnded D). none of these

56). The union of any collection of open sets is
 A). closed B). open C). bounded D). unbdunded
57). Intersection of finite collection of open sets is
 A). open B). closed C). bounded D). none of these
58). A set s id closed $$\Leftrightarrow$$
 A). $$\overline{s}=s$$ B). $$s\ne s$$ C). $$s < s$$ D). $$s>s$$
59). Compact implies
 A). bounded only B). closed only C). closed and bounded D). none of these
60). In Euclidean space $$R^{k}$$ every cauchy sequence is
 A). convergent B). divergent C). bounded D). none of these
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