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 productXn is a Lindel?f (resp. locally Lindel?f) space, then the space SPnX is also Lindel?f (resp. locally Lindel?f). We also prove that if the product Xn is a weakly Lindel?f (resp. weakly locally Lindel?f) space, then the space SPnX is also weakly Lindel?f (resp. weakly locally Lindel?f). Moreover, we investigate the preservation of the network weight, ?-character and local density of topological spaces by the functor of G-permutation degree. It is proved that this functor preserves the network weight, ?-character and local density of infinite topological T1-spaces.

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