Induced Mappings and Sequential Properties of the Space of G-Permutation Degree

In this paper, we study preservation of some mappings under the functor of G-permutation degree SP n G .We prove that if the mapping f : X → Y is almostopen (resp., pseudo-open, monotone), then the mapping, pseudo-open, monotone).In addition, we prove that the space X n is sequential (resp., Fréchet-Urysohn) if and only if the space SP n G X is sequential (resp.Fréchet-Urysohn).Also, we prove that if the space X n is strongly Fréchet-Urysohn, then the space SP n G X is also a strongly Fréchet-Urysohn space.

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