Some generalized metric properties of the space of G-permutation degree
In this paper we investigate some generalized metric properties of the space of G-permutation
degree SP n
G X. We prove that an infinite T 1 -space X has a σ-locally finite network if and only if the space
SP n
G X has a σ-locally finite network. We also establish that X has a σ-locally finite base if and only if SP
n
G X
has a σ-locally finite base. As an application, we obtain characterizations of metrizability and σ-spaces for
the space SP n
G X. Finally, we prove that an infinite regular space X is a P 0 -space if and only if SP
n
G X is a
P 0 -space.
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