Glasnik Matematicki, Vol. 53, No. 2 (2018), 371-384.

INVERSE COMPONENT CROPPING SEQUENCES AND CONNECTED INVERSE LIMITS OVER INTERVALS

Iztok Banič and Matevž Črepnjak

Faculty of Natural Sciences and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia
Institute of Mathematics, Physics and Mechanics, SI-1000 Ljubljana, Slovenia
Andrej Marušič Institute, University of Primorska, SI-6000 Koper, Slovenia
e-mail: iztok.banic@um.si

Faculty of Natural Sciences and Mathematics, University of Maribor, SI-2000 Maribor, Slovenia,
Faculty of Chemistry and Chemical Engineering, University of Maribor, SI-2000 Maribor, Slovenia,
Andrej Marušič Institute, University of Primorska, SI-6000 Koper, Slovenia
e-mail: matevz.crepnjak@um.si

Abstract.   We give a characterization of inverse sequences with upper semicontinuous bonding functions fi:[0,1] ⊸ [0,1] for which the inverse limit of the inverse sequence with fi-1 as bonding functions is connected. As a byproduct, we obtain another characterization of connected inverse limits of inverse sequences with a single bonding function.

2010 Mathematics Subject Classification.   54C60, 54B10, 54D80, 54F65, 54B99

Key words and phrases.   Inverse limits, upper semicontinuous functions, connectedness, component cropping sequences, inverse component cropping sequences

Full text (PDF) (free access)

DOI: 10.3336/gm.53.2.09

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