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1. • CommentRowNumber1.
   • CommentAuthorUrs
   • CommentTimeAug 20th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexstub entry, for the moment just so as to record references <a href="https://ncatlab.org/nlab/revision/equivariant+Tietze+extension+theorem/1">v1</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Tietze+extension+theorem">current</a>

   stub entry, for the moment just so as to record references

   v1, current

2. • CommentRowNumber2.
   • CommentAuthorUrs
   • CommentTimeAug 20th 2019
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded statement of the basic Tietze-Gleason extension theorem ([here](https://ncatlab.org/nlab/show/equivariant+Tietze+extension+theorem#TietzeGleasonExtensionTheorem)), as in [Palais 60, Theorem 1.4.3](https://ncatlab.org/nlab/show/equivariant+Tietze+extension+theorem#Palais60) <a href="https://ncatlab.org/nlab/revision/diff/equivariant+Tietze+extension+theorem/2">diff</a>, <a href="https://ncatlab.org/nlab/revision/equivariant+Tietze+extension+theorem/2">v2</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Tietze+extension+theorem">current</a>

   added statement of the basic Tietze-Gleason extension theorem (here), as in Palais 60, Theorem 1.4.3

   diff, v2, current

3. • CommentRowNumber3.
   • CommentAuthorUrs
   • CommentTimeMar 21st 2021
   • (edited Mar 21st 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexadded statement of other/more general conditions for the equivariant extension to exist (from [Jaworowski 76](https://ncatlab.org/nlab/show/equivariant+Tietze+extension+theorem#Jaworowski76), [Lashof 81](https://ncatlab.org/nlab/show/equivariant+Tietze+extension+theorem#Lashof81)): *** 1. the ambient [[domain]] [[G-space]] $X$ is 1. [[locally compact topological space|locally comact]] 1. [[separable topological space|separable]] 1. [[metrizable topological space|metrizable]] 1. finite-dimensional (?) 1. with a [[finite number]] of [[orbit type|orbit types]]. 1. the [[codomain]] [[G-space]] is such that * for every $G$-[[orbit type]] $(H)$ in the [[complement]] $X \setminus A$ the [[fixed locus]] $E^H$ is an [[absolute neighbourhood retract]]. *** <a href="https://ncatlab.org/nlab/revision/diff/equivariant+Tietze+extension+theorem/7">diff</a>, <a href="https://ncatlab.org/nlab/revision/equivariant+Tietze+extension+theorem/7">v7</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Tietze+extension+theorem">current</a>

   added statement of other/more general conditions for the equivariant extension to exist (from Jaworowski 76, Lashof 81):

   ---

   1. the ambient domain G-space $X$ is

      1. locally comact

      2. separable

      3. metrizable

      4. finite-dimensional (?)

      5. with a finite number of orbit types.

   2. the codomain G-space is such that

   • for every $G$-orbit type $(H)$ in the complement $X \setminus A$ the fixed locus $E^H$ is an absolute neighbourhood retract.

   ---

   diff, v7, current

4. • CommentRowNumber4.
   • CommentAuthorUrs
   • CommentTimeMar 21st 2021
   • PermaLink
   Author: Urs
   Format: MarkdownItexhave further expanded out the statement of the "Jaworowski extension theorem" ([here](https://ncatlab.org/nlab/show/equivariant+Tietze+extension+theorem#JaworowskiExtensionTheorem)), following Lashof. <a href="https://ncatlab.org/nlab/revision/diff/equivariant+Tietze+extension+theorem/8">diff</a>, <a href="https://ncatlab.org/nlab/revision/equivariant+Tietze+extension+theorem/8">v8</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Tietze+extension+theorem">current</a>

   have further expanded out the statement of the “Jaworowski extension theorem” (here), following Lashof.

   diff, v8, current

5. • CommentRowNumber5.
   • CommentAuthorUrs
   • CommentTimeMar 21st 2021
   • (edited Mar 21st 2021)
   • PermaLink
   Author: Urs
   Format: MarkdownItexfixed the condition on $A\subset X$: it needs to be a (closed) sub-$G$-space of $X$, not necessarily a subspace of $X^G$ (Palais60 and Lashof81 and many other authors say "invariant subspace", which is ambiguous -- but checking in Jaworowski clarifies it) <a href="https://ncatlab.org/nlab/revision/diff/equivariant+Tietze+extension+theorem/9">diff</a>, <a href="https://ncatlab.org/nlab/revision/equivariant+Tietze+extension+theorem/9">v9</a>, <a href="https://ncatlab.org/nlab/show/equivariant+Tietze+extension+theorem">current</a>

   fixed the condition on $A\subset X$: it needs to be a (closed) sub-$G$-space of $X$, not necessarily a subspace of $X^G$

   (Palais60 and Lashof81 and many other authors say “invariant subspace”, which is ambiguous – but checking in Jaworowski clarifies it)

   diff, v9, current