Displaying similar documents to “Some extensions of Banach's contraction principle in complete cone metric spaces.”

On a weak form of uniform convergence

Jaroslav Fuka, Petr Holický (2005)

Commentationes Mathematicae Universitatis Carolinae

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The notion of Δ -convergence of a sequence of functions is stronger than pointwise convergence and weaker than uniform convergence. It is inspired by the investigation of ill-posed problems done by A.N. Tichonov. We answer a question posed by M. Katětov around 1970 by showing that the only analytic metric spaces X for which pointwise convergence of a sequence of continuous real valued functions to a (continuous) limit function on X implies Δ -convergence are σ -compact spaces. We show that...