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Glasgow Mathematical Journal (1)

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NEIGHBORHOODS OF STRATA IN MANIFOLD STRATIFIED SPACES
BRUCE HUGHES
Journal:

Glasgow Mathematical Journal / Volume 46 / Issue 1 / January 2004

Published online by Cambridge University Press:

15 January 2004, pp. 1-28

Print publication:

January 2004
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Strata in manifold stratified spaces are shown to have neighborhoods that are teardrops of manifold stratified approximate fibrations (under dimension and compactness assumptions). This is the best possible version of the tubular neighborhood theorem for strata in the topological setting. Applications are given to replacement of singularities, to the structure of neighborhoods of points in manifold stratified spaces, and to spaces of manifold stratified approximate fibrations.