3.9. (a) Let K = {1/n ? ? | n ? ?_+}. Show that the standard topology on K is the discrete topology. (b) Let K* = K ? {0}. Show that the standard topology on K* is not the discrete topology.

          3.9. (a) Let K = {1/n ? ? | n ? ?_+}. Show that the standard topology on K is the discrete topology.
(b) Let K* = K ? {0}. Show that the standard topology on K* is not the discrete topology.

Added by Sarah E.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Vincenzo Zaccaro

03/14/2023

Step 1

- \( K = \left\{ \frac{1}{n} \mid n \in \mathbb{Z}^+ \right\} \) where \( \mathbb{Z}^+ \) is the set of positive integers. Show more…

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3.9. (a) Let K = {1/n ∈ ℝ | n ∈ ℤ₁}. Show that the standard topology on K is the discrete topology. (b) Let K* = K ∪ {0}. Show that the standard topology on K* is not the discrete topology.