some results in metric modular spaces

A metric modular on a set x is a function w: (0, ∞) × x × x → [0, ∞] written as (λ, x, y) 7→ wλ(x, y) satisfying, for all x, y, z ∈ x, the following three properties: x = y if and only if wλ(x, y) = 0 for all λ > 0; wλ(x, y) = wλ(y, x) for all λ > 0; wλ+µ(x, y) ≤ wλ(x, z) + wµ(y, z) for all λ, µ > 0. in this paper we define a hausdorff topology on metric modular spaces and prove some known results of metric spaces including baire’s theorem and uniform limit theorem for metric modular spaces.