Quasiopen and <Emphasis Type="Italic">p</Emphasis>-Path Open Sets,and Characterizations of Quasicontinuity |
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| Authors: | Anders Björn Jana Björn Jan Malý |
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| Institution: | 1.Department of Mathematics,Link?ping University,Link?ping,Sweden;2.Department of Mathematics, Faculty of Science,J. E. Purkyně University,ústí nad Labem,Czech Republic |
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| Abstract: | In this paper we give various characterizations of quasiopen sets and quasicontinuous functions on metric spaces. For complete metric spaces equipped with a doubling measure supporting a p-Poincaré inequality we show that quasiopen and p-path open sets coincide. Under the same assumptions we show that all Newton-Sobolev functions on quasiopen sets are quasicontinuous. |
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