Let X be a metric space and t: X to X be a map that...

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Advance Math

Let X be a metric space and t: X to X be a map that preservesdistances: d(t(x), t(y)) = d(x, y). Give an example in whicht isnot bijective.
Could let t: x to x+1,x non-negative, but how does this mean tis not surjective?
Any help will be much appreciated!

Answer & Explanation Solved by verified expert

4.4 Ratings (1120 Votes)

Note That Every distance preserving map are injective but notnecessarily bijective That means Distance preserving map need notto be surjective in this See Answer

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Let X be a metric space and t: X to X be a map that...

70.2K

Verified Solution

Question

Advance Math

Let X be a metric space and t: X to X be a map that preservesdistances: d(t(x), t(y)) = d(x, y). Give an example in whicht isnot bijective.
Could let t: x to x+1,x non-negative, but how does this mean tis not surjective?
Any help will be much appreciated!

Answer & Explanation Solved by verified expert

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Let X be a metric space and t: X to X be a map that...

70.2K

Verified Solution

Question

Advance Math

Let X be a metric space and t: X to X be a map that preservesdistances: d(t(x), t(y)) = d(x, y). Give an example in whicht isnot bijective.Could let t: x to x+1,x non-negative, but how does this mean tis not surjective?Any help will be much appreciated!

Answer & Explanation Solved by verified expert

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Other questions asked by students

Let X be a metric space and t: X to X be a map that preservesdistances: d(t(x), t(y)) = d(x, y). Give an example in whicht isnot bijective.
Could let t: x to x+1,x non-negative, but how does this mean tis not surjective?
Any help will be much appreciated!