Title

A Degree of Nonlocal Connectedness

Abstract

To any continuum X weassign an ordinal number (or the symbol ∞) s(X), called the degree of nonlocal connectedness of X. We show that (1) the degree cannot be increased under continuous surjections; (2) for hereditarily unicoherent continua X, the degree of a subcontinuum of X is less than or equal to s(X); (3) s(C(X)) ≤ s(X), where C(X) denotes the hyperspace of subcontinua of a continuum X. We also investigate the degrees of Cartesian products and inverse limits. As an application weconstruct an uncountable family of metric continua X homeomorphic to C(X).

Department(s)

Mathematics and Statistics

Keywords and Phrases

cartesian product; continuum; degree; hereditarily unicoherent; inverse limit; locally connected; ordinal number

Library of Congress Subject Headings

Hyperspace

Document Type

Article - Journal

Document Version

Citation

File Type

text

Language(s)

English

Rights

© 2001 Rocky Mountain Math Consortium, All rights reserved.

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