Vol. 95, No. 2, 1981

Recent Issues
Vol. 305: 1  2
Vol. 304: 1  2
Vol. 303: 1  2
Vol. 302: 1  2
Vol. 301: 1  2
Vol. 300: 1  2
Vol. 299: 1  2
Vol. 298: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Editorial Board
Subscriptions
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Author Index
To Appear
 
Other MSP Journals
𝜀-covering dimension

Allan Calder, William H. Julian, Ray Mines, III and Fred Richman

Vol. 95 (1981), No. 2, 257–262
Abstract

A compact metric space T has Lebesgue covering dimension at most n if for each positive 𝜀 the space T has an 𝜀-cover of order at most n. We show that if T is a compact subset of Euclidean n-space and T has an 𝜀-cover of order at most n 2, then any two points whose distance from T is greater than 𝜀 can be joined by a path bounded away from T. This refines, and provides a constructive proof for, the theorem that the complement of an (n 2)-dimensional compact subset of Euclidean n-space is connected.

Mathematical Subject Classification 2000
Primary: 54F45
Milestones
Received: 20 June 1980
Published: 1 August 1981
Authors
Allan Calder
William H. Julian
Department of Mathematical Sciences
New Mexico State University
Las Cruces NM 88003
United States
Ray Mines, III
Fred Richman