# Implicit functions from locally convex spaces to Banach spaces

Studia Mathematica (1999)

- Volume: 134, Issue: 3, page 235-250
- ISSN: 0039-3223

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topHiltunen, Seppo. "Implicit functions from locally convex spaces to Banach spaces." Studia Mathematica 134.3 (1999): 235-250. <http://eudml.org/doc/216636>.

@article{Hiltunen1999,

abstract = {We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller $C_Π^k$-map f defined on an open subset of E×F and with values in F, for E an arbitrary Hausdorff locally convex space and F a Banach space. As an application, we prove that under a certain transversality condition the preimage of a submanifold is a submanifold for a map from a Fréchet manifold to a Banach manifold.},

author = {Hiltunen, Seppo},

journal = {Studia Mathematica},

keywords = {implicit functions; locally convex spaces; Banach spaces},

language = {eng},

number = {3},

pages = {235-250},

title = {Implicit functions from locally convex spaces to Banach spaces},

url = {http://eudml.org/doc/216636},

volume = {134},

year = {1999},

}

TY - JOUR

AU - Hiltunen, Seppo

TI - Implicit functions from locally convex spaces to Banach spaces

JO - Studia Mathematica

PY - 1999

VL - 134

IS - 3

SP - 235

EP - 250

AB - We first generalize the classical implicit function theorem of Hildebrandt and Graves to the case where we have a Keller $C_Π^k$-map f defined on an open subset of E×F and with values in F, for E an arbitrary Hausdorff locally convex space and F a Banach space. As an application, we prove that under a certain transversality condition the preimage of a submanifold is a submanifold for a map from a Fréchet manifold to a Banach manifold.

LA - eng

KW - implicit functions; locally convex spaces; Banach spaces

UR - http://eudml.org/doc/216636

ER -

## References

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- [3] M. W. Hirsch, Differential Topology, Springer, New York, 1976.
- [4] H. H. Keller, z Differential Calculus in Locally Convex Spaces, Lecture Notes in Math. 417, Springer, Berlin, 1974.
- [5] A. Kriegl, Eine kartesisch abgeschlossene Kategorie glatter Abbildungen zwischen beliebigen lokalkonvexen Vektorräumen, Monatsh. Math. 95 (1983), 287-309.
- [6] A. Kriegl and P. W. Michor, z Aspects of the theory of infinite dimensional manifolds, Differential Geom. Appl. 1 (1991), 159-176. Zbl0782.58011
- [7] S. Lang, Differential Manifolds, Springer, New York, 1988.
- [8] U. Seip, Kompakt erzeugte Vektorräume und Analysis, Lecture Notes in Math. 273, Springer, Berlin, 1972. Zbl0242.46003

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