On the Extension of Homeomorphisms on the Interior of a Two Cell

نویسنده

  • E. E. FLOYD
چکیده

The subject under discussion in this paper is the study of the existence and properties of extensions of homeomorphisms of the interior I of a two cell with boundary C onto a plane bounded region. Particular emphasis will be placed on the action of the extension on C. Application of the topological results will then be made to conformai maps on the interior of the unit circle. The hypothesis that ƒ (J) = R is a homeomorphism of the interior I of a two cell with boundary C onto a plane bounded region R with boundary F(R) will be assumed throughout the paper. The usual terminology of transformation theory will be used : the transformation g(A)=B is said to be light if each f"(x)} # £ 5 , is totally disconnected, and non-alternating if for each x, yÇzB, f~(x) does not separate/~'(y).

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تاریخ انتشار 2007