Wijsman topology on function spaces |
| |
Authors: | Giuseppe Di Maio ubica Holà |
| |
Affiliation: | (1) Istituto di Matematica, Seconda Università di Napoli Piazza Duomo, 81100 Caserta, Italy;(2) Institute of Mathematics, Slovak Academy of Sciences Stefanikova, 49-81473 Bratislava, Slovakia |
| |
Abstract: | LetC(X,Y) be the space of continuous functions from a metric space (X,d) to a metric space (Y, e).C(X, Y) can be thought as subset of the hyperspaceCL(X×Y) of closed and nonempty subsets ofX×Y by identifying each element ofC(X,Y) with its graph. We considerC(X,Y) with the topology inherited from the Wijsman topology induced onCL(X×Y) by the box metric ofd ande. We study the relationships between the Wijsman topology and the compact-open topology onC(X,Y) and also conditions under which the Wijsman topology coincide with the Fell topology. Sufficient conditions under which the compactopen topology onC(X,Y) is weaker than the Wijsman topology are given (IfY is totally bounded, then for every metric spaceX the compactopen topology onC(X,Y) is weaker than the Wijsman topology and the same is true forX locally connected andY rim-totally bounded). We prove that a metric spaceX is boundedly compact iff the Wijsman topology onC(X, ℝ) is weaker than the compact-open topology. We show that ifX is a σ-compact complete metric space andY a compact metric space, then the Wijsman topology onC(X,Y) is Polish. |
| |
Keywords: | KeywordHeading" >Mathematics Subject Classification (1991) 54B05 54E35 54CO5 54B20 |
本文献已被 SpringerLink 等数据库收录! |
|