We prove that if X is a compact topological space which contains a nontrivial metrizable connected closed subset, then the vector lattice C(X) does not carry any sygma-Lebesgue topology.
@article{urn:eudml:doc:38769, title = {Les topologies sygma-Lebesgue sur C(X).}, journal = {Extracta Mathematicae}, volume = {19}, year = {2004}, pages = {313-316}, zbl = {1082.46004}, mrnumber = {MR2135827}, language = {fr}, url = {http://dml.mathdoc.fr/item/urn:eudml:doc:38769} }
Aqzzouz, Belmesnaoui; Nouira, Redouane. Les topologies sygma-Lebesgue sur C(X).. Extracta Mathematicae, Tome 19 (2004) pp. 313-316. http://gdmltest.u-ga.fr/item/urn:eudml:doc:38769/