Geodesic
More on Convergence of Continuous Functions and Topological Convergence of Sets
Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 52-59

Voir la notice de l'article provenant de la source Cambridge University Press

Let C(X, Y) denote the set of continuous functions from a metric space X to a metric space Y. Viewing elements of C(X, Y) as closed subsets of X × Y, we say {fn } converges topologically to f if Li fn = Lsfn = f. If X is connected, then topological convergence in C(X,R) does not imply pointwise convergence, but if X is locally connected and Y is locally compact, then topological convergence in C(X, Y) is equivalent to uniform convergence on compact subsets of X. Pathological aspects of topological convergence for seemingly nice spaces are also presented, along with a positive Baire category result.
DOI : 10.4153/CMB-1985-004-9
Mots-clés : 40A30, 54C35, 54B20, Topological convergence of sets, pointwise convergence, uniform convergence on compact subsets, equicontinuity, Kuratowski convergence of sets 
Beer, Gerald. More on Convergence of Continuous Functions and Topological Convergence of Sets. Canadian mathematical bulletin, Tome 28 (1985) no. 1, pp. 52-59. doi: 10.4153/CMB-1985-004-9
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