"It has been shown that topological spaces are characterized as quasi-pseudometric spaces over some Tikhonov semifield.
Sufficient conditions are given for a T1 space to be metrizable over some Tikhonov semifield.
Completely regular (uniform) spaces are characterized as pseudornetric spaces over some Tikhonov semifield.
Certain metric, pseudornetric, quasi-metric, quasipseudometric spaces over a Tikhonov semifield are shown to be respectively metric, pseudometric, quasi-metric, quasipseudometric spaces in the usual sense.
Several results from fixed point theory in the metric space setting are generalized to the setting of completely regular (uniform) Hausdorff spaces."--Abstract, page ii.
Hicks, Troy L.
Hatfield, Charles, 1920-1993
Pursell, Lyle E.
Oakes, Robert A.
Mathematics and Statistics
Ph. D. in Mathematics
University of Missouri--Rolla
iv, 54 pages
© 1972 Ronald Evans Satterwhite, All rights reserved.
Dissertation - Open Access
Fixed point theory
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Satterwhite, Ronald Evans, "Quasi-pseudometrics over Tikhonov semifields and fixed point theorems" (1972). Doctoral Dissertations. 184.