Some remarks providing discontinuous maps on some $C_p\left(X\right)$ spaces

S. 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 -