On transversality with deficiency

and a conjecture of Sard

Authors:
Carlos Biasi and Osamu Saeki

Journal:
Trans. Amer. Math. Soc. **350** (1998), 5111-5122

MSC (1991):
Primary 57N75; Secondary 57R45, 55M10

MathSciNet review:
1458297

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a map between manifolds and a manifold. In this paper, by using the Sard theorem, we study the topological properties of the space of maps which satisfy a certain transversality condition with respect to in a weak sense. As an application, by considering the case where is a point, we obtain some new results about the topological properties of , where is the set of points of where the rank of the differential of is less than or equal to . In particular, we show a result about the topological dimension of , which is closely related to a conjecture of Sard concerning the Hausdorff measure of .

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Additional Information

**Carlos Biasi**

Affiliation:
Departamento de Matemática, ICMSC-USP, Caixa Postal 668, 13560-970, São Carlos, SP, Brazil

Email:
biasi@icmsc.sc.usp.br

**Osamu Saeki**

Affiliation:
Department of Mathematics, Faculty of Science, Hiroshima University, Higashi- Hiroshima 739, Japan

Email:
saeki@top2.math.sci.hiroshima-u.ac.jp

DOI:
https://doi.org/10.1090/S0002-9947-98-02088-1

Received by editor(s):
November 14, 1996

Additional Notes:
The second author has been partially supported by CNPq, Brazil, and by the Grant-in-Aid for Encouragement of Young Scientists (no. 08740057), Ministry of Education, Science and Culture, Japan.

Article copyright:
© Copyright 1998
American Mathematical Society