Gruszecki, Lech A metrization of \(D_ E[0,1]\) space. (English) Zbl 0857.54027 Zesz. Nauk. Politech. Rzesz. 139, Mat. 18, 103-108 (1995). Given a metric space \((E,r)\), let \(D_E[0,1]\) denote the space of all \(E\)-valued functions on \([0,1]\) which are right continuous on \([0,1)\) and have left-side limits everywhere on \((0,1]\). Following the metrization of \(D_E[0,\infty)\) given in [S. N. Ethier and T. G. Kurtz, Markov processes, characterization and convergence (1986; Zbl 0592.60049)] the author introduces a new distance \(\rho\) in \(D_E[0,1]\) and shows that \(\rho\) determines a topology that is weaker than Skorokhod topology. Also, a condition for convergence in the Skorokhod topology is given. Reviewer: Z.Piotrowski (Youngstown) MSC: 54E35 Metric spaces, metrizability 60J99 Markov processes 26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable 54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.) Keywords:Markov process; metrization; Skorokhod topology Citations:Zbl 0592.60049 PDFBibTeX XMLCite \textit{L. Gruszecki}, Zesz. Nauk. Politech. Rzesz., Mat. 139(18), 103--108 (1995; Zbl 0857.54027)