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,…

Answered: A path is said to be closed if the…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.1: Rectangular Coordinate Systems

Problem 8E

See similar textbooks

Similar questions

False Let f be a mapping from ]0,1[ to ]0, 1[ defined by f(x) = x. Then * O f has a unique fixed point If(x)-f(y)Is2]x-yl and f has no fixed point. If(x)-f(y)Is2]x-yl and f has a fixed point. None of the choices. Let (X,T) be a comapct space and A be a subset of X. If A is closed, then A compact. True arch TOSH IRA
(1) a suubase for a top not. (2) a base (b) Let X=(2,3,5,8) with indiscrete topology and Y=(a, b,c) with discrete, let f be a constant map from a space X into a space Y show that whether f is: (1) continuous map or not. (2) open map or not. (3) closed map or not.
or not. (c) Let f be a map from a space(X,T), into a space (Y,T) and t,t;such that TSt and TS ,, show that whether if f is T---t open map then fis t-? open map or not. open map or not, and if f is t--- t open map then f is t--
Example : - Let f: (Z,+,.)→ (Z/(3), +, .) be a function s. t. f(a) = a + (3), Va EZ. Show that fis epimorphism and find the Ker.f.
ull alfa 4G 2:46 PM @ 0 73% A docs.google.com Let f be a mapping from [1,+0[ to [1,+00[, defined by f(x)=x+1/x. Then * f is continuous but it is not a homeomorphism None of the choices f is not continuous f is a homeomorphism Let X and Y be two discrete spaces, then * X is homeomorphic to Y if and only if X and Y are both finite X is homeomorphic to Y if and only if X and Y have the same cardinality X is never homeomorphic to Y X is homomorphic to Y if and only if X and Y are both infinite
{a,d}, {a,e}}, then * (X,T) is not connected but it is Hausdorff (X, T) is neither Hausdorff nor connected (X, T) is not Hausdorff but it is connected (X,T) is Hausdorff and connected Let (X,T) and (Y,T1) be two topological spaces and let f be a continuous mapping of X into Y. * None of the choices If f is one to one and (Y,T1) is a T1-space, then (X,T) is a T1-space If (Y,T1) is a Hausdorff space, then (X,T) is a Hausdorff space If f is onto and (Y,T1) is a T1-space, then (X,T) is a T1-space Let f be a mapping from [1,+0[ to [1,+00[, defined by f(x)=x+1/ en f is neither continuous nor a
Theorem Let f be a continuous function on an open subset U of a Banach space X into a Banach space Y. Let a and b by any distinct points in U such that the segment [a, b] is contained in U and f be differentiable at each point of [a, b]. Let g be any continuous linear function on X into Y. Then || ƒ (b)-f(a) - g (b-a) || ≤c|| b-all, where c is a real number such that || Df (x) - g || ≤c, for all x in [a, b].
Let X=(7,8,9,. and A-(8,9] and metric defined on X as d(x.y) |= |x-y Give the last answer Find interior of A (1) Find limit points of A (2) Find open ball B(7.2) (3) explain if A is dense or not (4) explain if A is closed or not (5)
let (X,T) be a topological space. Then a function f is continuous at x0 element of X if and only if f is both lower semi continuous and upper semi continuous at x0 element of X.
(5.8) Symmetric Bilinear Maps: Let f:V x V F is bilinear map, then f is called symmetric if f(A, B) = f(B, A), VA, B E V.
Let X={2,3,4,...} and A= {3,4,5} and metric defined on |X as d(x,y) = |x - y Give the last answer Find interior of A (1) Find limit points of A (2) Find open ball B(2,3) (3) explain if A is dense or (4) not explain if A is closed or (5) not
True or False: The set of all functions f(t) such that f(t+4)3D f(t) forms a linear space. O True O False

SEE MORE QUESTIONS

Recommended textbooks for you

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

Algebra & Trigonometry with Analytic Geometry

Algebra

ISBN:

9781133382119

Author:

Swokowski

Publisher:

Cengage

SEE MORE TEXTBOOKS