Suppose that R (the set of real numbers) is equipped by TO (the Euclidean topology), T1 (the discrete topology) and T2 (the finite closed topology). Then la,b[ is: * not open in any of TO, T1 and T2 O open in TO but not open in T1 and T2 O open is TO and T1 but not open in T2 O open in TO, T1 and T2

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.3: Properties Of Composite Mappings (optional)
Problem 8E: Suppose f,g and h are all mappings of a set A into itself. a. Prove that if g is onto and fg=hg,...
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Suppose that R (the set of real numbers) is
equipped by TO (the Euclidean topology), T1
(the discrete topology) and T2 (the finite
closed topology). Then Ja,b[ is:
not open in any of T0, T1 and T2
open in TO but not open in T1 and T2
open is TO and T1 but not open in T2
O open in TO, T1 and T2
Transcribed Image Text:Suppose that R (the set of real numbers) is equipped by TO (the Euclidean topology), T1 (the discrete topology) and T2 (the finite closed topology). Then Ja,b[ is: not open in any of T0, T1 and T2 open in TO but not open in T1 and T2 open is TO and T1 but not open in T2 O open in TO, T1 and T2
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