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We prove that every Baire subspace Y of c₀(Γ) has a dense $G_{\delta }$ metrizable subspace X with dim X ≤ dim Y. We also prove that the Kimura-Morishita Eberlein compactifications of metrizable spaces preserve large inductive dimension. The proofs rely on new and old results concerning the dimension of uniform spaces.

We construct in ZFC a cosmic space that, despite being the union of countably many metrizable subspaces, has covering dimension equal to 1 and inductive dimensions equal to 2.

The fundamental properties of approximate inverse systems of uniform spaces are established. The limit space of an approximate inverse sequence of complete metric spaces is the limit of an inverse sequence of some of these spaces. This has an application to the dimension of the limit space of an approximate inverse system. A topologically complete space with $dim\le n$ is the limit of an approximate inverse system of metric polyhedra of $dim\le n$. A completely metrizable separable space with $dim\le n$ is the limit of an...

Short proofs of the fact that the limit space of a non-gauged approximate system of non-empty compact uniform spaces is non-empty and of two related results are given.

For each natural number n ≥ 1 and each pair of ordinals α,β with n ≤ α ≤ β ≤ ω(⁺), where ω(⁺) is the first ordinal of cardinality ⁺, we construct a continuum $S_{n,\alpha ,\beta }$ such that (a) $dim{S}_{n,\alpha ,\beta }=n$; (b) $trDg{S}_{n,\alpha ,\beta }=trDgo{S}_{n,\alpha ,\beta }=\alpha$; (c) $trind{S}_{n,\alpha ,\beta }=trInd₀S_{n,\alpha ,\beta }=\beta$; (d) if β < ω(⁺), then $S_{n,\alpha ,\beta }$ is separable and first countable; (e) if n = 1, then $S_{n,\alpha ,\beta }$ can be made chainable or hereditarily decomposable; (f) if α = β < ω(⁺), then $S_{n,\alpha ,\beta }$ can be made hereditarily indecomposable; (g) if n = 1 and α = β < ω(⁺), then $S_{n,\alpha ,\beta }$ can be made chainable and hereditarily indecomposable. In particular,...