Person: Serrano Pascual, Feliciana
Universidad Complutense de Madrid
Faculty / Institute
Geometría y Topología
Now showing 1 - 3 of 3
- PublicationTopología de las gráficas en espacios de funciones continuas(Universidad Complutense de Madrid, 2015) Serrano Pascual, Feliciana; Outerelo Domínguez, Enrique
- PublicationWhitney topology and normality(Elsevier Science, 1993-08) Serrano Pascual, FelicianaI.I. Guran and M.M. Zarichnyi proved that C(X,Y) with the Whitney topology is not normal provided that X and Y are manifolds of positive dimension and X noncompact. We obtain a similar result for spaces of continuous functions between more general topological spaces, giving in some cases necessary and sufficient conditions for C(X,Y) to be normal.
- PublicationNon normality of R R with the graph topology(Symposium of General Topology, 1988) Serrano Pascual, FelicianaAuthor 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.