RT Journal Article
T1 Non normality of R R with the graph topology
A1 Serrano Pascual, Feliciana
AB Author considers the subspaces of Y X which consists of almost continuous functions. (A function is almost continuous if every neighbourhood of its graph contains the graph of some continuous function. [S. A. Naimpally, Trans. Am. Math. Soc. 123, 267-272 (1966). All function spaces are provided by graph topology, which is stronger than Tikhonov's one and weaker then box one [loc. cit.].Main results are: Theorem 9. The space of all almost continuous functions in R R whose graphs are dense in R 2 is not regular with respect to the graph topology. Theorem 11. There exists a function in R R (not continuous) that can not be separated from the closed set of all connected graphs, in graph topology. These theorems answer some questions from L. B. Lawrence, Houston J. Math. 13, 389-403 (1987). It was shown, that the space of all almost continuous functions from R to R is not connected in graph topology.
PB Symposium of General Topology
SN 0918-4732
YR 1988
FD 1988
LK https://hdl.handle.net/20.500.14352/58681
UL https://hdl.handle.net/20.500.14352/58681
DS Docta Complutense
RD 6 may 2024