Equicharacter of uniform and topological spaces (Q1183660)

The author introduces metric equicharacter for uniform spaces and proves that the class of uniform spaces having metric equicharacter is closed under sums, quotients and products. Then using another approach, she reproves some results on equicharacter due to \textit{H. Pfister} [General Topol. Appl. 7, 261-273 (1977; Zbl 0362.54021)], mainly that equicharacter does not exceed covering character and that equicharacter of a product is the supremum of equicharacters of the coordinate spaces. The last part deals with equicharacter of topological spaces defined as equicharacter of the corresponding fine uniformity. It is proved that a product or a \(\sigma\)-product of separable spaces has countable equicharacter; unlike uniform spaces, equicharacter of topological spaces does not behave well on products and dense subspaces.