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