Search results for "Open mapping"

Mappings of finite distortion: discreteness and openness for quasi-light mappings

2005

Abstract Let f ∈ W 1 , n ( Ω , R n ) be a continuous mapping so that the components of the preimage of each y ∈ R n are compact. We show that f is open and discrete if | D f ( x ) | n ⩽ K ( x ) J f ( x ) a.e. where K ( x ) ⩾ 1 and K n − 1 / Φ ( log ( e + K ) ) ∈ L 1 ( Ω ) for a function Φ that satisfies ∫ 1 ∞ 1 / Φ ( t ) d t = ∞ and some technical conditions. This divergence condition on Φ is shown to be sharp.

Set-Valued Generalizations of Baire′s Category Theorem

1995

Abstract We prove some generalizations of Baire′s category theorem for chains of iterates of multifunctions defined on Cech-complete spaces. In particular, we extend Lennard′s results stated for functions on complete metric spaces.

A property of connected Baire spaces

1997

Abstract We give a topological version of a classical result of F. Sunyer Balaguer's on a local characterization of real polynomials. This is done by studying a certain property on a class of connected Baire spaces, thus allowing us to obtain a local characterization of repeated integrals of analytic maps on Banach spaces.

Injective spaces of real-valued functions with the baire property

1995

Generalizing the technique used by S.A. Argyros in [3], we give a lemma from which certain Banach spaces are shown to be non-injective. This is applied mainly to study the injectivity of spaces of real-valued Borel functions and functions with the Baire property on a topological space. The results obtained in this way do not follow from previous works about this matter.

Existence theorems for m-accretive operators in Banach spaces

2005

Abstract In 1985, the second author proved a surjective result for m -accretive and ϕ -expansive mappings for uniformly smooth Banach spaces. However, in this case, we have been able to remove the uniform smoothness of the Banach space, without any additional assumption.

A theorem of insertion and extension of functions for normal spaces

1993

Linearization of holomorphic mappings on fully nuclear spaces with a basis

1994

In [13] Mazet proved the following result.If U is an open subset of a locally convex space E then there exists a complete locally convex space (U) and a holomorphic mapping δU: U→(U) such that for any complete locally convex space F and any f ɛ ℋ (U;F), the space of holomorphic mappings from U to F, there exists a unique linear mapping Tf: (U)→F such that the following diagram commutes;The space (U) is unique up to a linear topological isomorphism. Previously, similar but less general constructions, have been considered by Ryan [16] and Schottenloher [17].

A rank theorem for analytic maps between power series spaces

1994

Existence theorems for inclusions of the type

1999

For a family of operator inclusions with convex closed-valued right-hand sides in Banach spaces, the existence of solutions is obtained by chiefly using Ky Fan's fixed point principle. The main result of the paper improves Theorem 1 in [16] as well as Theorem 2.2 of [3]. Some meaningful concrete cases are also presented and discussed.