Ascoli-Arzelà-Theory based on continuous convergence in an (almost) non-Hausdorff setting

René Bartsh, Peter Dencker and Harry Poppe
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René Bartsh: University of Rostock, Dept. of Mathematics
Peter Dencker: University of Rostock, Dept. of Mathematics
Harry Poppe: University of Rostock, Dept. of Mathematics

A chapter in Categorical Topology, 1996, pp 221-240 from Springer

Abstract: Abstract In the sixties and at the beginning of the seventies by H. Poppe was constructed a unified approach to compactness criteria in topological and uniform functionspaces, especially in spaces of continuous functions. The main tools used for this approach were convergence spaces, generalized uniform spaces (based on coverings) and for the function spaces the convergence structure of continuous convergence. These constructions and results were summarized in the book [8]. From the recent papers and books where Ascoli-Arzelà theory is treated we want to mention: W. Gähler [1], J.W. Gray [2], H. Herrlich [3], R.A. McCoy and J. Ntantu [4], K. Morita [5], L.D. Nel [6], H. Render [11], [12].

Keywords: 54C35; 54D30; 54D50; 54E15; Relatively compact sets; continuous convergence; compactness on function spaces; compactness criteria of Ascoli-Arzelà-type; even continuity; equicontinuity; compact-open topology; uniform topology. (search for similar items in EconPapers)
Date: 1996
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-009-0263-3_20

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DOI: 10.1007/978-94-009-0263-3_20

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