Unicoherence In Topological Spaces

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Doctor of Arts (D.A.)


This exposition is a research monograph containing all the fundamental results concerning unicoherence of topological spaces. It is also a survey and a guide to the literature on unicoherence.Since the material is treated from a historical prospective we state the theorems for the most part in the order in which they were originally proven. For convenience of exposition sometimes results and ideas are combined. The theorems are usually stated in the same form in which they appeared in the original paper.The first mathematicians who used the concept of unicoherence were Vietoris and C. Kuratowski in 1926. The earliest important characterizations of unicoherence were given by C. Kuratowski in 1928-29, K. Borsuk in 1931-33, W. A. Wilson in 1933, E. Cech in 1933 and S. Eilenberg in 1935-36. Later, other important results of unicoherence were developed by A. D. Wallace in 1942, A. H. Stone in 1949, H. Miller in 1950, J. J. Charatonik in 1964, R. F. Dickman in 1967 and 1972-73, S. Nadler in 1970-71, D. Bennett in 1971, and J. H. V. Hunt in 1974 and 1980.



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