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- W2080322671 abstract "In [6] Whyburn made the following conjecture and verified it for the case n=2: Supposef is a light open mapping of one n-cell onto another. Iff maps the boundary homeomorphically, thenf is a loomeomorphism. If f C'C, the truth of the conjecture follows from the structure theorem of P. T. Church [1]. The question is still open in the general case. The purpose of this note is to affirm the conjecture for fCC2; however, it is not required thatf be light. DEFINITIONS. For f: X-> Y, X and Y topological spaces, f is open if f( U) is open for every U open in X; f is light if f(p) is totally disconnected for every p $f(X). Let Bf denote the set of all x CX such thatf is not a local homeomorphism at x. If X is an open subset of En, Euclidean n-space, and Y is open in Em, let R&(f) be the set of all xCX such that the rank of the Jacobian matrix of f at x is less than or equal to j, 0 Eo such that Fl Dn =f and F has continuous second order partial derivatives in U." @default.
- W2080322671 created "2016-06-24" @default.
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- W2080322671 date "1968-03-01" @default.
- W2080322671 modified "2023-09-26" @default.
- W2080322671 title "Whyburn’s conjecture for $Csp{2}$ maps" @default.
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- W2080322671 doi "https://doi.org/10.1090/s0002-9939-1968-0226604-9" @default.
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