Vol. 94, No. 2, 1981

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ISSN: 0030-8730
Completely regular absolutes and projective objects

Raymond Frank Dickman, Jack Ray Porter and Leonard Rubin

Vol. 94 (1981), No. 2, 277–295

The absolute (EX,πX) is constructed for an arbitrary space X and is shown to be unique with respect to EX being extremally disconnected and completely regular and πX being a 𝜃-continuous, perfect, separating irreducible surjection. A function f : X Y is said to have a continuous E-lifting if there is a continuous function F : EX EY such that πY F = f πX. A class of functions, called η-continuous, is introduced, shown to contain the class of continuous functions and the class of 𝜃-continuous, closed surjections, and proved to have continuous E-liftings. Functions which have continuous E-liftings are completely characterized as being the composition of η-continuous functions.

Mathematical Subject Classification 2000
Primary: 54G05
Secondary: 54C05
Received: 8 February 1980
Revised: 29 May 1980
Published: 1 June 1981
Raymond Frank Dickman
Jack Ray Porter
Leonard Rubin