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added the reference David provided.
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edit approved Mar 19, 2021 at 18:26
Jesse Wolfson
edit approved Mar 19, 2021 at 18:26
Jesse Wolfson
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In fact, any Whitney stratified set admits a stratification in the sense of Thom/Mather, cf Mather's notes on topological stability, published in B.A.M.S Volume 49, Number 4, October 2012, Pages 475–506, cf section 8 in particuler p 492 : "Hence it follows from Proposition 7.1 that any Whitney stratified set admits the structure of an abstract stratified set."

Update: The affirmative answer appears as Proposition 3.2 of Quinn, "Homotopically Stratified Spaces" JAMS, 1988.

In fact, any Whitney stratified set admits a stratification in the sense of Thom/Mather, cf Mather's notes on topological stability, published in B.A.M.S Volume 49, Number 4, October 2012, Pages 475–506, cf section 8 in particuler p 492 : "Hence it follows from Proposition 7.1 that any Whitney stratified set admits the structure of an abstract stratified set."

In fact, any Whitney stratified set admits a stratification in the sense of Thom/Mather, cf Mather's notes on topological stability, published in B.A.M.S Volume 49, Number 4, October 2012, Pages 475–506, cf section 8 in particuler p 492 : "Hence it follows from Proposition 7.1 that any Whitney stratified set admits the structure of an abstract stratified set."

Update: The affirmative answer appears as Proposition 3.2 of Quinn, "Homotopically Stratified Spaces" JAMS, 1988.

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David C
David C
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In fact, any Whitney stratified set admits a stratification in the sense of Thom/Mather, cf Mather's notes on topological stability, published in B.A.M.S Volume 49, Number 4, October 2012, Pages 475–506, cf section 8 in particuler p 492 : "Hence it follows from Proposition 7.1 that any Whitney stratified set admits the structure of an abstract stratified set."