Exactly K-to-1 Maps: from Pathological Functions with Finitely Many Discontinuities to Well-behaved Covering Maps
نویسنده
چکیده
Many mathematicians encounter k-to-1 maps only in the study of covering maps. But, of course, k-to-1 maps do not have to be open. This paper touches on covering maps, and simple maps, but concentrates on ordinary k-to-1 functions (both continuous and finitely discontinuous) from one metric continuum to another. New results, old results, and ideas for further research are given; and a baker’s dozen of questions are raised.
منابع مشابه
Covering Systems and Periodic Arithmetical Functions
If the ring Z of integers is the union of finitely many residue classes a1(mod n1), . . . , ak(mod nk), then the system A = {as(mod ns)}s=1 is called a cover of Z or a covering system. There are many problems and results on this topic initiated by Paul Erdös. In this talk we introduce progress on the main open problems in this field, as well as the algebraic theory of periodic arithmetical maps...
متن کاملEntropy of a semigroup of maps from a set-valued view
In this paper, we introduce a new entropy-like invariant, named Hausdorff metric entropy, for finitely generated semigroups acting on compact metric spaces from a set-valued view and study its properties. We establish the relation between Hausdorff metric entropy and topological entropy of a semigroup defined by Bis. Some examples with positive or zero Hausdorff metric entropy are given. Moreov...
متن کاملChange Detection in Urban Area Using Decision Level Fusion of Change Maps Extracted from Optic and SAR Images
The last few decades witnessed high urban growth rates in many countries. Urban growth can be mapped and measured by using remote sensing data and techniques along with several statistical measures. The purpose of this research is to detect the urban change that is used for urban planning. Change detection using remote sensing images can be classified into three methods: algebra-based, transfor...
متن کاملStable Stationary Harmonic Maps to Spheres
Dedicated to Professor WeiYue Ding on the occasion of his 60th birthday Abstract For k ≥ 3, we establish new estimate on Hausdorff dimensions of the singular set of stable-stationary harmonic maps to the sphere S. We show that the singular set of stable-stationary harmonic maps from B to S is the union of finitely many isolated singular points and finitely many Hölder continuous curves. We also...
متن کاملMultifractal analysis for expanding interval maps with infinitely many branches
Abstract. In this paper we investigate multifractal decompositions based on values of Birkhoff averages of functions from a class of symbolically continuous functions. This will be done for an expanding interval map with infinitely many branches and is a generalisation of previous work for expanding maps with finitely many branches. We show that there are substantial differences between this ca...
متن کامل