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  3. a function f : x ------> y between two topologi

A function f : X ------> Y between two topological spaces ( X , TX )...

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Advance Math

A function f : X ------> Y between twotopological spaces ( X , TX ) and ( Y , TY ) iscalled a homeomorphism it has the followingproperties:

a) f is a bijection (one - to- one and onto)

b) f iscontinuous

c) the inverse fucntionf  -1 is continuous ( f is openmapping)

A function with these three properties is sometimes calledbicontinuous . if such a function exists, we say X and Y arehomeomorphic.

show that a complete metric space R is homeomorphic to themetric space ( 0 , 1 ), which is not complete . Metric defined asan ab solute value of the difference  

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Define a mapasa f is oneone and ontooneone forand hence is oneone isonto for take an arbitrary Then we find an such    See Answer
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