Harry Poppe

Ascoli-Arzela-Theory based on continuous convergence in an (almost) non-Hausdorff setting 2

The paper is published: Rostocker Mathematisches Kolloquium, Rostock. Math. Kolloq. 72, 35 - 48 (2019/2020)

MSC: 54C35 Function spaces in general topology
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
54D30 Compactness
46A20 Duality theory for topological vector spaces
54C25 Embedding

Abstract:   We start with the paper [1] and thus come back to continuous convergence and to the characterization of compactness with respect to this convergence structure for the space C(X, Y ) of continuous functions, where X and Y are topological spaces. More generally we can use for X, Y convergence spaces, as was done for instance in [11] and [15]. But in the first paper of this title X and Y were topological spaces and we will continue with this assumption.
[1] Bartsch, R., Dencker, P., and Poppe, H. : Ascoli-Arzela -Theory based on contin- uous convergence in an (almost) non-Hausdorff setting. Categorial Topology, E. Guli, ed., Kluwer Academic Publisher, Dordrecht 1996, 221 – 240
[11] Mynard, F. : A convergence-theoretic Viewpoint on the Arzela-Ascoli theorem. Real. Anal. Exch. 38, No. 2, 2013, 431 – 444
[15] Poppe, H. : Compactness in General Function Spaces. Deutscher Verlag der Wissenschaften, Berlin 1974

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