Glasnik Matematicki, Vol. 54, No. 2 (2019), 463-476.

Δ-RELATED FUNCTIONS AND GENERALIZED INVERSE LIMITS

Tina Sovič

Faculty of Civil Engineering, Transportation Engineering and Architecture, University of Maribor, 2000 Maribor, Slovenia
e-mail: tina.sovic@um.si

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

2010 Mathematics Subject Classification.   54F15, 54C60

Key words and phrases.   Inverse limits, upper semicontinuous functions, quotient maps

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

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