Cardinality of inverse limits with upper semicontinuous bonding functions

Authors

  • M. Roskaric University of Maribor
  • N. Tratnik University of Maribor

Keywords:

Continua, Limits, Inverse limits, Cardinality, Upper semicontinuous set valued functions

Abstract

We explore cardinality of generalised inverse limits. Among other things we show that for any \(n\in \{ \aleph_0, c, 1,2,3, \ldots\}\) there is an upper semicontinuous function with the inverse limit having exactly \(n\) points. We also prove that if \(f\) is an upper semicontinuous function whose graph is a continuum, then the cardinality of the corresponding inverse limit is either 1, \(\aleph_0\) or \(c\). This generalises the recent result of I. Banic and J. Kennedy, which claims the same is true in the case when the graph is an arc. DOI: 10.1017/S0004972714000689

Published

2014-11-13

Issue

Vol. 91 No. 1 (2015)

Section

Articles
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