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Let X be a completely regular Hausdorff topological space and $C_{p} (X)$ the space of continuous real-valued maps on X endowed with the pointwise topology. A simple and natural argument is presented to show how to construct on the space $C_{p} (X)$ , if X contains a homeomorphic copy of the closed interval [0,1], real-valued maps which are everywhere discontinuous but continuous on all compact subsets of $C_{p} (X)$ .

Spaces with countable $s n$ -networks

Ge Ying (2004)

Commentationes Mathematicae Universitatis Carolinae

In this paper, we prove that a space $X$ is a sequentially-quotient $π$ -image of a metric space if and only if $X$ has a point-star $s n$ -network consisting of $c s^{*}$ -covers. By this result, we prove that a space $X$ is a sequentially-quotient $π$ -image of a separable metric space if and only if $X$ has a countable $s n$ -network, if and only if $X$ is a sequentially-quotient compact image of a separable metric space; this answers a question raised by Shou Lin affirmatively. We also obtain some results on spaces with countable...

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Semi-closed sets and the associated topology

Sequentially continuous mappings of product spaces

Singular arc-like continua [Book]

Some characterizations of bitopological connectivity properties

Some observations on local uniform boundedness principles

Some observations on local uniform boundedness principles. II

Some problems and lines of investigation in general topology

Some properties of oscillation

Some remarks providing discontinuous maps on some $C_{p} (X)$ spaces

Spaces with countable $s n$ -networks

Stackbases in power sets of neighbourhood spaces preserving the continuity of mappings

Stetige Funktionen auf dem Torus.

Sur la sommabilité de familles de fonctions uniformément continues

Sur les fonctions cliquish

Sur les sélecteurs des multifonctions

Currently displaying 1 – 15 of 15