An n-od (respectively, infinite-od) is a continuum X which has a subcontinuum K such that X\K has n components (respectively, infinitely many components). In 1944, Sorgenfrey proved that if a continuum X is the union of three subcontinua with a point in common and such that no one of the subcontinua is contained in the union of the other two, then X contains a triod. In this note a single simple proof is given for the obvious generalization of Sorgenfrey's theorem to n-ods and infinite-ods.
Copyright © 1989 Houston Journal of Mathematics. This article first appeared in Houston Journal of Mathematics 15:2 (1989), 245-247.
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Nall, Van C. "On the Presence of n-ods and Infinite-ods." Houston Journal of Mathematics 15, no. 2 (1989): 245-247.