This paper presents a method to construct a smooth seamless conformal surface for the genus-0 manifold. The method is developed for the conformal self-organizing map [10]. The constructed surface is both piecewise smooth and continuous. The mapping between the model surface and the sphere surface is one-to-one and onto. We show experiments in surface reconstruction and texture mapping.

Let X and A be compact metric spaces. The main problem studied in this paper is that of finding conditions under which a map f : A → X can be lifted to a cell-like space; i.e., conditions are sought under which there exist a cell-like continuum Z and continuous maps g : Z → X and f ′ : A → Z such that g ◦ f ′ = f . A theorem is proved which spells out technical conditions on the embedding of A ...

Let f : X → X be a map of a compact, connected Riemannian manifold, with or without boundary. For > 0 sufficiently small, we introduce an -Nielsen number N ( f ) that is a lower bound for the number of fixed points of all self-maps of X that are -homotopic to f . We prove that there is always a map g : X → X that is -homotopic to f such that g has exactlyN ( f ) fixed points. We describe proced...

Let X be a topological space and CL(X) the family of all nonempty closed subsets X. In this paper we discuss problem when continuous map between spaces induces function their respective hyperspaces. As main result characterize continuity induced in case Fell Attouch-Wets Additionally explore whether action group G on CL(X). particular give sufficient conditions topology to guarantee that is con...

We say that two unitary or orthogonal representations of a finitely generated group G are additive conjugates if they intertwined by an map, which need not be continuous. associate to each representation topological action is complete conjugacy invariant: the automorphisms on Bohr compactification underlying Hilbert space. Using this construction we show property having almost invariant vectors...