Geodesic
Minimality and Prehomogeneity
Acta mathematica Universitatis Comenianae, Tome 72 (2003) no. 2 
Samer Al Ghour. Minimality and Prehomogeneity. Acta mathematica Universitatis Comenianae, Tome 72 (2003) no. 2. http://geodesic.mathdoc.fr/item/AMUC_2003_72_2_a12/
@article{AMUC_2003_72_2_a12,
     author = {Samer Al Ghour},
     title = {Minimality and {Prehomogeneity}},
     journal = {Acta mathematica Universitatis Comenianae},
     year = {2003},
     volume = {72},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/AMUC_2003_72_2_a12/}
}
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We introduce two new types of minimality; Namely: minimal set and minimal preopen set. Several results concerning these types and the known type (minimal open set) are obtained. We also introduce prehomogeneity concept as a generalization of homogeneity. Several results concerning it are given, some of which related to minimality concepts. Various counter examples relevant to the relations obtained in this paper are given.