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∈{ℵ0,c,1,2,3,…} 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, ℵ0 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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