# Some remarks providing discontinuous maps on some ${C}_{p}\left(X\right)$ spaces

Banach Center Publications (2008)

- Volume: 79, Issue: 1, page 131-133
- ISSN: 0137-6934

## Access Full Article

top## Abstract

top## How to cite

topS. Moll. "Some remarks providing discontinuous maps on some $C_p(X)$ spaces." Banach Center Publications 79.1 (2008): 131-133. <http://eudml.org/doc/282240>.

@article{S2008,

abstract = {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 $C_\{p\}(X)$.},

author = {S. Moll},

journal = {Banach Center Publications},

keywords = {compact space; completely regular space; continuous real-valued map; spaces of continuous functions},

language = {eng},

number = {1},

pages = {131-133},

title = {Some remarks providing discontinuous maps on some $C_p(X)$ spaces},

url = {http://eudml.org/doc/282240},

volume = {79},

year = {2008},

}

TY - JOUR

AU - S. Moll

TI - Some remarks providing discontinuous maps on some $C_p(X)$ spaces

JO - Banach Center Publications

PY - 2008

VL - 79

IS - 1

SP - 131

EP - 133

AB - 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 $C_{p}(X)$.

LA - eng

KW - compact space; completely regular space; continuous real-valued map; spaces of continuous functions

UR - http://eudml.org/doc/282240

ER -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.