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

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

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

a) Prove that τ is a topology.

b) Is {−4, −3, −2, −1, 0, 1, 2, 3, 4} compact in this topology?

c) Is it connected?

d) Is Z compact in this topology?

e) Is it connected?

Expert Solution

Colby Messinger answered 1 year ago

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Question

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

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