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  3. on z we consider the family of sets ? = {z, ?, {?1

On Z we consider the family of sets ? = {Z, ?, {?1, 0, 1},...

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Advance Math

On Z we consider the family of sets ? = {Z, ?, {?1, 0, 1}, {?2,?1, 0, 1, 2}, . . . }

where the dots mean all sets like the two before that.

a) Prove that ? is a topology.

b) Is {?4, ?3, ?2, ?1, 0, 1, 2, 3, 4} compact in thistopology?

c) Is it connected?

d) Is Z compact in this topology?

e) Is it connected?

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