Local Properties of Maps of the Ball
نویسنده
چکیده
Let f be an essential map of Sn−1 into itself (i.e., f is not homotopic to a constant mapping) admitting an extension mapping the closed unit ball B n into Rn. Then, for every interior point y of Bn, there exists a point x in f −1(y) such that the image of no neighborhood of x is contained in a coordinate half space with y on its boundary. Under additional conditions, the image of a neighborhood of x covers a neighborhood of y. Differential versions are valid for quasianalytic functions. These results are motivated by game-theoretic considerations.
منابع مشابه
On the pointfree counterpart of the local definition of classical continuous maps
The familiar classical result that a continuous map from a space $X$ to a space $Y$ can be defined by giving continuous maps $varphi_U: U to Y$ on each member $U$ of an open cover ${mathfrak C}$ of $X$ such that $varphi_Umid U cap V = varphi_V mid U cap V$ for all $U,V in {mathfrak C}$ was recently shown to have an exact analogue in pointfree topology, and the same was done for the familiar cla...
متن کاملSynthesis of CuO Nanoparticles and Study on their Catalytic Properties
In this research, CuO spherical-like nanoparticles were synthesized using the planetary ball mill method. The structure, particle size and morphology of the resulting CuO nanoparticles were characterized by XRD (X-ray diffraction), SEM (scanning electron microscopy) and SAXS (small-angle X-ray scattering) methods. The results of this investigation showed ...
متن کاملDefects and Structural Analysis of Multi-Wall Carbon Nano Tubes via Ball milling and Cryo-milling
Nano fillers are part of new studies to enhance various properties of fluids and solids. For example, adding nanoparticles as an enforcement in nanocomposites or as an additive to improve thermal or electrical properties in nano-fluids are of extreme importance in science and industry. There are numerous methods to uniformly disperse nanoparticles in fluid and solid phase. One of the well-used ...
متن کاملThe Effect of Rotation Speed and Time of Milling on Synthesis and Properties of Fluoridated Hydroxyapatite Biomaterial
Synthetic hydroxyapatite (HA) is the most helpful because of its similarity to natural bone in both crystalline structure and chemical composition. Recently, fluoridated hydroxyapatite (FHA) has been developed in dental and orthopedic application because it has lower solubility than pure HA, while maintaining the comparable bioactivity and biocompatibility. The aim of this study was to...
متن کاملModeling of Hydrodynamic Factors for Management of Coastal Hazards, Case Study: Khamir Port, Persian Gulf, Iran
In coastal areas, hydrodynamic factors make changes in shorelines geomorphology. This can affect coastal facilities and cause hazards to human societies in the areas. This study has investigated the influence of wave and tide properties on Khamir Port, Hormoz Strait in coast of Persian Gulf. The purpose of the study is to make a mathematical regional and local modeling of water level fluctuatio...
متن کامل