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. Please be as clear as possible and if necessary showing the definitions.
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. Please be as clear as possible and if necessary showing the definitions.
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.2: Vector Spaces
Problem 38E: Determine whether the set R2 with the operations (x1,y1)+(x2,y2)=(x1x2,y1y2) and c(x1,y1)=(cx1,cy1)...
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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.
Please be as clear as possible and if necessary showing the definitions.
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