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Displaying 21 – 26 of 26

Spaces not distinguishing convergences

Miroslav Repický (2000)

Commentationes Mathematicae Universitatis Carolinae

In the present paper we introduce a convergence condition $(Σ^{'})$ and continue the study of “not distinguish” for various kinds of convergence of sequences of real functions on a topological space started in [2] and [3]. We compute cardinal invariants associated with introduced properties of spaces.

Spaces not distinguishing pointwise and $ℐ$ -quasinormal convergence

Pratulananda Das, Debraj Chandra (2013)

Commentationes Mathematicae Universitatis Carolinae

In this paper we extend the notion of quasinormal convergence via ideals and consider the notion of $ℐ$ -quasinormal convergence. We then introduce the notion of $ℐ Q N (ℐ w Q N)$ space as a topological space in which every sequence of continuous real valued functions pointwise converging to $0$ , is also $ℐ$ -quasinormally convergent to $0$ (has a subsequence which is $ℐ$ -quasinormally convergent to $0$ ) and make certain observations on those spaces.

Strict Uniformity in Ergodic Theory.

Georges Hansel (1973/1974)

Mathematische Zeitschrift

Stronger topologies preserving the class of continuous functions

Helena Nonas (1978)

Fundamenta Mathematicae

Sums of quasicontinuous functions

Ján Borsík (1993)

Mathematica Bohemica

It is proved that every real cliquish function defined on a separable metrizable space is the sum of three quasicontinuous functions.

Sur deux espaces de fonctions non dérivables

Robert Cauty (1992)

Fundamenta Mathematicae

Let D (resp. D*) be the subspace of C = C([0,1], R) consisting of differentiable functions (resp. of functions differentiable at the one point at least). We give topological characterizations of the pairs (C, D) and (C, D*) and use them to give some examples of spaces homeomorphic to CDor to CD*.

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