Original scientific paper

https://doi.org/10.3336/gm.54.2.09

Δ-related functions and generalized inverse limits

Tina Sovič ; Faculty of Civil Engineering, Transportation Engineering and Architecture, University of Maribor, 2000 Maribor, Slovenia

Abstract

For any continuous single-valued functions \(f,g: [0,1] \rightarrow [0,1]\) we define upper semicontinuous set-valued functions \(F,G: [0,1] \multimap [0,1]\) by their graphs as the unions of the diagonal \(\Delta\) and the graphs of set-valued inverses of \(f\) and \(g\) respectively. We introduce when two functions are \(\Delta\)-related and show that if \(f\) and \(g\) are \(\Delta\)-related, then the inverse limits \(\varproj F\) and \(\varproj G\) are homeomorphic. We also give conditions under which \(\varproj G\) is a quotient space of \(\varproj F\).

Keywords

Inverse limits; upper semicontinuous functions; quotient maps

Hrčak ID:

229606

URI

https://hrcak.srce.hr/229606

Publication date:

11.12.2019.

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