TRANSCRIBE THE FOLLOWING TEXT IN DIGITAL FORMAT (12)A path is said to be closed if the function thatgenerates it satisfies f(0) = f(1)we have to show, being closed is a topological property.Topological Property :The properties of a topological space that arepreserved under a homeomorphism are known astopological property. Example - Connectedness, compactness.●andLet Y: XY be a homeomorphismf: [0, 1] → x be a closed path in x .Then f(0) = f(1).Then yof: [0, 1] → Y is a closed path in Y.Note that yof is continuous as the compositionof two continuous functions is continuousNext,Yof (0) = 4 (f (0)) = † (f (1)) = * of (1)Similarly, for any closed path 8:[0,1] →Y, wecan say 4 to 8 [0,1] → X is a closed path in X.beingclosed path is a topological propertyHence

A path is said to be closed if the function that generates it satisfies f(0) = f (1). we have to show, being closed is a topological Topological Property : The properties of a topological space that are preserved under a homeomorphism are known as topological property. Example - Connectedness, compactness. topological property. and Let Y: XY be a homeomorphism f: [0,1] →→x be a closed path in x . Then f(0) = f(1). Then yof: [0, 1]→Y is a closed path in Y. Note that yof is continuous as the composition of two continuous functions is continuous Next, Yof (0) = 4 (f(0)) = † (ƒ(1)) = * •f (1) of Similarly, for any closed path S: [0, 1] →Y, we can say 4 to 8 [0, 1] → X is a closed path in X. ; Hence, being a closed path is a topological property Y

A path is said to be closed if the function that generates it satisfies f(0) = f (1). we have to show, being closed is a topological Topological Property : The properties of a topological space that are preserved under a homeomorphism are known as topological property. Example - Connectedness, compactness. topological property. and Let Y: XY be a homeomorphism f: [0,1] →→x be a closed path in x . Then f(0) = f(1). Then yof: [0, 1]→Y is a closed path in Y. Note that yof is continuous as the composition of two continuous functions is continuous Next, Yof (0) = 4 (f(0)) = † (ƒ(1)) = * •f (1) of Similarly, for any closed path S: [0, 1] →Y, we can say 4 to 8 [0, 1] → X is a closed path in X. ; Hence, being a closed path is a topological property Y

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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