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  3. the following are true or false statements. if tru

The following are True or False statements. If True, give a simple justi?cation. If False, justify, or...

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Advance Math

The following are Trueor False statements. If True, give a simple justi?cation. If False,justify, or better, give a counterexample.

1. (R,discrete) is acomplete metric space.
2. (Q,discrete) is a compact metric space.
3. Every continuous function from R to R maps an interval to aninterval.

4. The set {(x,y,z) :x2 ?y3 + sin(xy) < 2} is open inR3

Answer & Explanation Solved by verified expert
4.5 Ratings (981 Votes)
TRUESupposebe a cauchy sequence inIn discrete spacefor all Sincebe a cauchy sequence so if we choosethen there existsuch that for all but since for allso for all That is the sequenceis an eventually constant sequence that is thereexistsuch that for allfor    See Answer
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