Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Sequential decreasing strong size properties

Sequential decreasing strong size properties AbstractLet X be a continuum. The n-fold hyperspace Cn(X), n < ∞, is the space of all nonempty closed subsets of X with at most n components. A topological property P$ \mathcal{P} $ is said to be a (an almost) sequential decreasing strong size property provided that if μ is a strong size map for Cn(X, {tj}j=1∞$ \{t_{j}\}_{j=1}^{\infty} $ is a sequence in the interval (t,1) such that lim tj = t ∈ [0,1) (t ∈ (0,1)) and each fiber μ−1(tj) has property P$ \mathcal{P} $, then so does μ−1(t). In this paper we show that the following properties are sequential decreasing strong size properties: being a Kelley continuum, local connectedness, continuum chainability and, unicoherence. Also we prove that indecomposability is an almost sequential decreasing strong size property. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematica Slovaca de Gruyter

Sequential decreasing strong size properties

Loading next page...
 
/lp/de-gruyter/sequential-decreasing-strong-size-properties-GO8rdxnYMZ

References

References for this paper are not available at this time. We will be adding them shortly, thank you for your patience.

Publisher
de Gruyter
Copyright
© 2018 Mathematical Institute Slovak Academy of Sciences
ISSN
0139-9918
eISSN
1337-2211
DOI
10.1515/ms-2017-0176
Publisher site
See Article on Publisher Site

Abstract

AbstractLet X be a continuum. The n-fold hyperspace Cn(X), n < ∞, is the space of all nonempty closed subsets of X with at most n components. A topological property P$ \mathcal{P} $ is said to be a (an almost) sequential decreasing strong size property provided that if μ is a strong size map for Cn(X, {tj}j=1∞$ \{t_{j}\}_{j=1}^{\infty} $ is a sequence in the interval (t,1) such that lim tj = t ∈ [0,1) (t ∈ (0,1)) and each fiber μ−1(tj) has property P$ \mathcal{P} $, then so does μ−1(t). In this paper we show that the following properties are sequential decreasing strong size properties: being a Kelley continuum, local connectedness, continuum chainability and, unicoherence. Also we prove that indecomposability is an almost sequential decreasing strong size property.

Journal

Mathematica Slovacade Gruyter

Published: Oct 25, 2018

Keywords: Primary 54C05, 54C10, 54B20; Secondary 54B15; n -fold hyperspace; strong size property; strong size map; Kelley continuum; indecomposability; local connectedness; continuum chainability and unicoherence

References