(3) Consider the topological space (R. 7), where T= {UCR: U = 0 or R\U is countable}. (a) Show that T is a topology on R. (b) Show that in (R, 7), any two non-empty open sets have non-empty intersection.
(3) Consider the topological space (R. 7), where T= {UCR: U = 0 or R\U is countable}. (a) Show that T is a topology on R. (b) Show that in (R, 7), any two non-empty open sets have non-empty intersection.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(3) Consider the topological space (R, T), where
T = {U CR: U = 0 or R \ U is countable}.
(a) Show that T is a topology on R.
(b) Show that in (R, 7), any two non-empty open sets have non-empty
intersection.
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