engleski

The Lelek Fan as the Inverse Limit of Intervals with a Single Set-Valued Bonding Function Whose Graph is an Arc

We consider a family of inverse limits of inverse sequences of closed unit intervals with a single upper semi-continuous set-valued bonding function whose graph is an arc ; the graph is the union of two line segments in [0, 1]^2, both of which contain the origin (0, 0) and have positive slope. One of the segments extends to the top-boundary and the other to the right side boundary of [0, 1]×[0, 1]. We show that there is a large subfamily F of these bonding functions such that for each f ∈ F, the inverse limit of the inverse sequence of closed unit intervals using f as a single bonding function is homeomorphic to the Lelek fan.

Fan ; cantor fan ; Lelek fan ; closed relation ; Mahavier product ; inverse limit ; set-valued function

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