On the Fundamental Group of Inverse Limits

Article

Abstract

In this paper we study the fundamental group of inverse limits, obtained by upper semi-continuous set valued functions. We present a number of crucial examples which demonstrate the technical difficulties, related to the control of the fundamental group in the inverse limit. Furthermore, these examples realize some important groups as the fundamental groups of inverse limits: free groups and the Hawaiian Earring group. On the other hand, we introduce the right shift of a loop in the inverse limit and prove that the fundamental group of an inverse limit, which is a one-dimensional Peano continuum, is often trivial or uncountable.

Keywords

Inverse limits Set valued functions Fundamental group 

Mathematics Subject Classification

54C60 54D80 

Notes

Acknowledgments

This research was supported by the Slovenian Research Agency Grants P1-0292-0101 and J1-6721-0101

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and PhysicsUniversity of LjubljanaLjubljanaSlovenia

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