Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Joint continuity of division of smooth functions. II. The distance to a Whitney stratified set from a transversal submanifold
HTML articles powered by AMS MathViewer

by Mark Alan Mostow PDF
Trans. Amer. Math. Soc. 292 (1985), 585-594 Request permission

Abstract:

Let $S$ be a closed set in ${{\mathbf {R}}^m}$, and let a ${C^1}$ Whitney stratification of $S$ be given. (Actually, only Whitney (a)-regularity is needed.) Let $f:{{\mathbf {R}}^n} \to {{\mathbf {R}}^m}$ be a ${C^1}$ map transversal to all the strata. Assume that the image of $f$ intersects $S$. Then for each compact set $K$ in ${{\mathbf {R}}^n}$, the Euclidean distances $\rho (x,{f^{ - 1}}(S))$ and $\rho (f(x),S)$, for $x$ in $K$, are bounded by constant multiples of each other. The bounding constants can be chosen to work for all maps $g$ which are close enough to $f$ in a ${C^1}$ sense on a neighborhood of $K$. This result is used in part I (written jointly with S. Shnider) to prove a result on the joint continuity of the division of smooth functions [MS].
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 58C25
  • Retrieve articles in all journals with MSC: 58C25
Additional Information
  • © Copyright 1985 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 292 (1985), 585-594
  • MSC: Primary 58C25
  • DOI: https://doi.org/10.1090/S0002-9947-1985-0808739-7
  • MathSciNet review: 808739