ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. LXXIII, 2 (2004)
p. 187 - 196
Components and Local Prehomogeneity
S. al Ghour

Abstract.  Prehomogeneous components are introduced. Then the concept of local prehomogeneity as a generalization of both prehomogeneity and local homogeneity is introduced. As a generalization of local prehomogeneity, the concept of prelocal prehomogeneity is also introduced. Many results concerning these concepts are obtained. Several counter examples regarding the relations obtained in this paper are given. Many open questions are also proposed.
Keywords: Homogeneous and prehomogeneous components, minimal preopen sets, homogeneity and local homogeneity, prehomogeneity and local prehomogeneity, generated topologies  

AMS Subject classification:  54B, 54C.
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