Does there exists a homeomorphisms which are not isometries,but preserves completeness??

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Does there exists a homeomorphisms which are not isometries,but preserves completeness??

The above question clicked my mind while studying the relations

$1)$Isometry$\implies$ Homeomorphism$\implies$ Continuity

$2)$ Isometry preserves Completeness.

I searched lot in books but do not get any result...Please give some suggestions