论文信息 - THE ENCLOSING OF CELLS IN THREE SPACE BY SIMPLE CLOSED SURFACES

THE ENCLOSING OF CELLS IN THREE SPACE BY SIMPLE CLOSED SURFACES

arc or simple closed curve in R3 with a certain property 1' (defined below) has a complement which is homeomorphic to the complement of its prototype, an evident necessary condition for being tame. In this paper an extension of the definition of property 'P to k-cells in RI, k = 1, 2, or 3, is made, and an extension of the result of Harrold to k-cells is made at the cost of imposing an extra condition which is always fulfilled when k = 1. The techniques used are those of Harrold, and depend strongly on the results of Alexander [1]. Much use is made of the concept of a semi-linear

H. C. Griffith

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