Regulating Hartshorne’s connectedness theorem

Extension of the Douady-Hubbard's Theorem on Connectedness of the Mandelbrot Set to Symmetric Polynimials

A Connectedness Theorem for Real Spectra of Polynomial Rings

Let R be a real closed field. The Pierce-Birkhoff conjecture says that any piecewise polynomial function f on Rn can be obtained from the polynomial ring R[x1, . . . , xn] by iterating the operations of maximum and minimum. The purpose of this paper is twofold. First, we state a new conjecture, called the Connectedness conjecture, which asserts the existence of connected sets in the real spectr...

extension of the douady-hubbard's theorem on connectedness of the mandelbrot set to symmetric polynimials

Proof of a Folklore Julia Set Connectedness Theorem and Connections with Elliptic Functions

We prove the following theorem about Julia sets of the maps fn,p,γ(z) = z n + γ zp , for integers n, p ≥ 2, γ ∈ C by using techniques developed for the Weierstrass elliptic ℘ function and adapted to this setting. Folklore connectedness theorem: If fn,p,γ has a bounded critical orbit, then J(fn,p,γ) is connected. This is related to connectivity results by the author and others about J(℘), where ...

Detecting connectedness.

Natural visual images are typically composed of multiple objects, which need to be segregated from each other and from the background. The visual system has evolved to capture a great variety of cues that allow a meaningful segmentation of the visual input. One of these cues is connectedness. Connected image regions are likely to belong to a single visual object, whereas disconnected image regi...