Normalizer of the group of unit intervalsegment $C^\infty$ diffeomorphisms in the group of unit intervalsegment homeomorphisms

What is the normalizer of the group of $C^\infty$ diffeomorphisms on $[0, 1]$, with multiplicationgroup law given by composition, in the group of all homeomorphisms onof $[0, 1]$?

If the answer is known, is there some "elementary" proof for the result?

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edited Dec 9, 2023 at 7:23

YCor

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clarified title and question

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edited Dec 9, 2023 at 2:08

Todd Trimble

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Normalizer of $C^\infty[0,1]$the group of unit interval diffeomorphisms in $C^0[0,1]$the group of unit interval homeomorphisms

What is the normalizer of the group of diffeomorphisms on $C^\infty[0,1]$$[0, 1]$, with multiplication given by composition, in the group of all homeomorphisms on $C^0[0,1]$$[0, 1]$? IsIf the answer is known, is there some "elementary" proof for the result?

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asked Dec 8, 2023 at 12:21

Henry

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Normalizer of the group of unit intervalsegment $C^\infty$ diffeomorphisms in the group of unit intervalsegment homeomorphisms

Normalizer of the group of unit interval diffeomorphisms in the group of unit interval homeomorphisms

Normalizer of the group of segment $C^\infty$ diffeomorphisms in the group of segment homeomorphisms

Normalizer of $C^\infty[0,1]$the group of unit interval diffeomorphisms in $C^0[0,1]$the group of unit interval homeomorphisms

Normalizer of $C^\infty[0,1]$ in $C^0[0,1]$

Normalizer of the group of unit interval diffeomorphisms in the group of unit interval homeomorphisms