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Journal of Convex Analysis, Vol. 6, No. 1, pp. 29-40 (1999)
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Topological Properties of a New Graph Topology

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P. Brandi and R. Ceppitelli and L$'$. Hola

Department of Mathematics, University of Perugia, Via L. Vanvitelli 1, 06100 Perugia, Italy, e-mail: mateas@unipg.it and Department of Mathematics, University of Perugia, Via L. Vanvitelli 1, 06100 Perugia, Italy, matagria@dipmat.unipg.it and Academy of Sciences, Institut of Mathematics, Stefanikova 49, 81 473 Bratislava, Slovakia, hola@mau.savba.sk

**Abstract:** In [10, 11, 12] a new graph topology $\tau$ was introduced which is useful in applications to differential equations. In this paper we study topological properties of $\tau$ and relations between $\tau$ and other known topologies. For example, we find conditions under which $\tau$ coincides with Back's generalized compact-open topology successfully used for convergence of utility functions [2] and for convergence of dynamic programming models [19].

**Keywords:** Kuratowski convergence, $\tau$-convergence, Back's convergence

**Classification (MSC2000):** 54C35, 54B20, 34K05

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