Normal covers of infinite products and normality of Σ-products

We give some characterizations for normal covers of infinite products of generalized metric spaces such as M-spaces, Σ-spaces and β-spaces. We prove them simultaneously in terms of β-spaces and perfect maps. Next, we give affirmative answers to two questions concerning the normality of Σ-products, which were raised by the author and Yamazaki, respectively. These results are stated in terms of Σ-products of β-spaces.