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Connected properties of the sublinear Higson corona of $\Bbb R^n$

Yuji Akaike

Abstract

In this paper, for the $n$-dimensional Euclidean space $\Bbb R^n$ with the usual metric and $n\geq2$, we show that the sublinear Higson corona of $\Bbb R^n$ is not locally connected at any point and is mutually aposyndetic.

Connected properties of the sublinear Higson corona of $\Bbb R^n$

Abstract

In this paper, for the -dimensional Euclidean space with the usual metric and , we show that the sublinear Higson corona of is not locally connected at any point and is mutually aposyndetic.
Paper Structure (3 sections, 10 theorems, 19 equations)

This paper contains 3 sections, 10 theorems, 19 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Non local connectedness and mutual aposyndesis of $\nu_L\Bbb R^n$

Key Result

Proposition 2.1

Let $\alpha X$ be a compactification of a noncompact completely regular space $X$. Then the following conditions are equivalent$:$

Theorems & Definitions (18)

  • Proposition 2.1
  • Proposition 2.2: DS
  • Lemma 2.3: DS
  • Definition 2.4
  • Definition 2.5
  • Proposition 2.6: DS
  • Lemma 2.7
  • proof
  • Lemma 2.8
  • proof
  • ...and 8 more