Browsing by Author "Kuykendall, Daniel P."
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Item Irreducibility in inverse limits of continua(1971) Kuykendall, Daniel P.; Ingram, William T.; Cook, Howard; Traylor, D. Reginald; Vobach, Arnold R.; Kern, John W.This paper gives characterizations of irreducibility, indecomposability, and hereditary indecomposability for inverse limits of compact metric continua; the characterizations are in terms of the bonding maps. The characterization of indecomposability is used to get a characterization, in terms of covers, for indecomposability in any compact metric continuum. The latter result is applied to circle-like continua to got a characterization of indecomposability in terms of defining sequences of covers.Item Irreducibility in inverse limits of intervals(1969) Kuykendall, Daniel P.; Ingram, William; Cook, Howard; Kern, John W.This paper is concerned chiefly with inverse limit systems in which each space in the system is an interval, although some of the theorems are proved in a more general setting. It is shown in Theorem 10 that an inverse limit of intervals, with the restriction that all the functions in the inverse limit system involved be the same, is irreducible between some two points. Theorem 11 gives a necessary and sufficient condition for an inverse limit of intervals to be irreducible between each two of some three points.