Abstract
In this paper, we give some properties of $$z^\circ $$ -ideals in intermediate rings of C(X) (i.e., subrings of C(X) containing $$C^*(X)$$ ). Moreover, some characterizations of almost P-spaces via intermediate rings of C(X) are established. Using these, we investigate answers to the two questions concerning $$z^\circ $$ -ideals in intermediate rings raised in Bag et al. (Appl Gen Topol 20(1): 109–117, 2019).
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