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TOPOLOGIES AND INCIDENCE STRUCTURE ON Rn-GEOMETRIES
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 Title & Authors
TOPOLOGIES AND INCIDENCE STRUCTURE ON Rn-GEOMETRIES
Im, Jang-Hwan;
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 Abstract
An R -geometry (P , L) is a generalization of the Euclidean geometry on R (see Def. 1.1). We can consider some topologies (see Def. 2.2) on the line set L such that the join operation V : P P \ longrightarrow L is continuous. It is a notable fact that in the case n = 2 the introduced topologies on L are same and the join operation V : P P \ longrightarrow L is continuous and open [10, 11]. It is a fundamental topological property of plane geometry, but in the cases n 3, it is no longer true. There are counter examples [2]. Hence, it is a fundamental problem to find suitable topologies on the line set L in an R -geometry (P , L) such that these topologies are compatible with the incidence structure of (P , L). Therefore, we need to study the topologies of the line set L in an R -geometry (P , L). In this paper, the relations of such topologies on the line set L are studied.
 Keywords
topological geometry;R -geometry;continuous and open maps;
 Language
English
 Cited by
1.
CONDITIONAL FEYNMAN INTEGRAL AND SCHRÖDINGER INTEGRAL EQUATION ON A FUNCTION SPACE, Bulletin of the Australian Mathematical Society, 2009, 79, 01, 1  crossref(new windwow)
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