2023-11-29T19:31:26Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/585442023-08-10T17:57:02Zcom_20.500.14352_14col_20.500.14352_15
00925njm 22002777a 4500
dc
Garrido, M. Isabel
author
Montalvo, Francisco
author
1994
Let C(X) denote the continuous real-valued functions on a topological space X . The question of whether a u -dense subring of C(X) is m -dense is studied in this note. Recall that neighborhoods of a function f in the u -topology are determined by an interval (f−ε,f+ε) for ε a positive number and in the m -topology by intervals (f−e,f+e) for u a positive unit in C(X) . J. Kurzweil [Studia Math. 14 (1954), 214–231, had shown that u -denseness and m -denseness are equivalent for subrings of C(X) closed under bounded inversion. Here, the authors prove that this result is not valid for arbitrary subrings of C(X) . In particular, they show that the property of every u -dense subring being m -dense is equivalent to X being pseudocompact
0213-8743
https://hdl.handle.net/20.500.14352/58544
http://dmle.cindoc.csic.es/pdf/EXTRACTAMATHEMATICAE_1994_09_01_07.pdf
http://www.eweb.unex.es/eweb/extracta/
Uniform density and m -density for subrings of C(X