In the Hyperbolic space Hn (n ≥ 3) there are uncountably many topological types of convex hypersurfaces. When is a locally convex hypersurface in Hn globally convex, that is, when does it bound a convex set? We prove that any locally convex proper embedding of an (n− 1)-dimensional connected manifold is the boundary of a convex set whenever the complement of (n−1)-flats of the resulting hypersu...

Throughout the sequel, E denotes a reflexive real Banach space and E∗ its topological dual. We also assume that E is locally uniformly convex. This means that for each x ∈ E, with ‖x‖ = 1, and each > 0, there exists δ > 0 such that, for every y ∈ E satisfying ‖y‖ = 1 and ‖x− y‖ ≥ , one has ‖x + y‖ ≤ 2(1 − δ). Recall that any reflexive Banach space admits an equivalent norm with which it is loca...

Institute of Mathematics of the Academy of Sciences of the Czech Republic provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use. This paper has been digitized, optimized for electronic delivery and stamped with digital signature within the project DML-CZ: The Czech Digital Mathematics Library 1 We show how some c...

We prove the following result. Let C be a convex compact subset in a topological vector space, and T : C → C a convex continuous mapping. (See Definition 1.1.) Then T has a fixed point. Moreover, continuous mappings that can be approximated by convex continuous mappings also have the fixed point property.

For a convex curve in an even-dimensional aane space we introduce a series of convex domains (called Young hulls) describe their structure and give a formulas for the volume of the biggest of these domains. A simple smooth curve in R m is called convex if the total multiplicity of its intersection with any aane hyperplane does not exceed m. Note that each convex curve is nondegen-erate, i.e. ha...

if we consider some special conditions, we can assume fundamental group of a topological space as a new topological space. in this paper, we will present a number of theorems in topological fundamental group related to semilocally simply connected property for a topological space.

This paper develops a geometric approach of variational analysis for the case of convex objects considered in locally convex topological spaces and also in Banach space settings. Besides deriving in this way new results of convex calculus, we present an overview of some known achievements with their unified and simplified proofs based on the developed geometric variational schemes.

In [1,2,3], A. C. Baker and J.W. Baker studied the subspace Ma(S) of the convolution measure algebra M, (S) of a locally compact semigroup. H. Dzinotyiweyi in [5,7] considers an analogous measure space on a large class of C-distinguished topological semigroups containing all completely regular topological semigroups. In this paper, we extend the definitions to study the weighted semigroup ...

Introduction. Some years ago Hausdorff, using Hamel bases, showed that any infinite dimensional real Banach space contained a second category linear subspace that was not complete under any equivalent norm [5]. It is shown below that a slight abstraction of his construction leads to the following: (A) a "multiple offender" example (Theorem 3), one that combines several pathological features whi...