Vol. 46, No. 2, 1973

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Proximity convergence structures

Ellen Elizabeth Reed

Vol. 46 (1973), No. 2, 471–485

In this paper the notion of proximity convergence structures is introduced. These constitute a layer between Cauchy structures and uniform convergence structures (in the sense of Cook and Fischer [1]). They are a natural generalization of proximity structures. A study of the relations among these various structures constitutes §§2 and 3. In §4, compact extensions for a special class of proximity convergence spaces are constructed, and a characterization of these is obtained. They satisfy a mapping property with respect to compact T2 proximity convergence spaces which satisfy a strong regularity condition. One problem left open is the obtaining of a more reasonable definition of regularity for these spaces.

Mathematical Subject Classification 2000
Primary: 54A20
Secondary: 54E05
Received: 24 February 1972
Published: 1 June 1973
Ellen Elizabeth Reed