Let X be a bounded subset of the real line and let Y be a metric space. In the function space C(X, Y), we give an intrinsic characterization of the functions f for which the neighborhood system in the Hausdorff topology coincides with the neighborhood system in the uniform convergence topology. (C) 2001 Elsevier Science B.V. All rights reserved.
On the Hausdorff Convergence of Functions of One Real Variable
MARCONI, UMBERTO
2001
Abstract
Let X be a bounded subset of the real line and let Y be a metric space. In the function space C(X, Y), we give an intrinsic characterization of the functions f for which the neighborhood system in the Hausdorff topology coincides with the neighborhood system in the uniform convergence topology. (C) 2001 Elsevier Science B.V. All rights reserved.
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