Some Topological and Cardinal Properties of the Space of Permutation Degree

In this paper, we prove a few facts and some cardinal properties of the space of permutation degree introduced in [6]. More precisely, we prove that if the product Xn is a Lindelof (resp. locally Lindelof) space, then the space SP"X is also Lindelof (resp. locally Lindelof). We also prove that if the product Xn is a weakly Lindelof (resp. weakly locally Lindelof) space, then the space SP"X is also weakly Lindelof (resp. weakly locally Lindelof). Moreover, we investigate the preservation of the network weight, 7t-character and local density of topological spaces by the functor of G-permutation degree. It is proved that this functor preserves the network weight, 7t-character and local density of infinite topological T1-spaces.