Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.7: Distinguishable Permutations And Combinations
Problem 29E
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We say that a space (X,τ) is connected if there exist two open non-empty spaces A,B such that A∩B≠∅ and A∪B=X. A space(X,τ) is connected if it does not satisfy the previous condition. Show that if the only subsets that are both open and closed are X and ∅ then the space is connected.
 
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