Wiginton, C. Lamar2022-06-222022-06-22196813673668https://hdl.handle.net/10657/9724Let S be a compact commutative topological semigroup and H a closed subsemigroup of S. If [chi] is a continuous unit-character of H, it is possible to obtain the following necessary and sufficient conditions for [chi] to be extendable to S. First, (x,y,a)[epsilon]HxhxS and xa = ya then [chi](x) = [chi](y). Also, (x,y)[epsilon]HxH and xe = ye then [chi](x) = [chi](y) where e is the least idempotent of S. Using these results, if [chi] is a continuous character of S, not necessarily a unit-character, further necessary and sufficient conditions for the extendability of [chi] are found. It is shown that [chi] can be extended to S if and only if there exists an open and closed prime ideal P such that H[intersection](SP) is the support of [chi], and if x and y are elements of the support and a an element of the complement of P with xa = ya then [chi](x) = [chi](y). From these conditions, other criteria for extendability can be derived with the additional hypothesis that S is a pseudo-invertible semigroup. Finally, results are obtained which show that, to seme extent, it suffices to consider continuous characters defined on closed subsemigroups of S which are unions of components of S. The results in this paper parallel those of R. O. Fulp in his recent paper bearing the same title.application/pdfenThis item is protected by copyright but is made available here under a claim of fair use (17 U.S.C. Section 107) for non-profit research and educational purposes. Users of this work assume the responsibility for determining copyright status prior to reusing, publishing, or reproducing this item for purposes other than what is allowed by fair use or other copyright exemptions. Any reuse of this item in excess of fair use or other copyright exemptions requires express permission of the copyright holder.Thesisreformatted digital