On R∞ and Q∞-manifolds

A topological characterization of LF-spaces

“…Put X 0 = Q and instead of the product Q × ⊡ n∈N X n consider the small box-product ⊡ n∈ω X n . In order to prove that ⊡ n∈ω X n is a Q × R ∞ -manifold, we shall apply Sakai's characterization [21] of open subspaces of Q × R ∞ , mentioned in the Introduction. We can assume that each space X n carries a uniformity that generates its topology.…”

Detecting topological groups which are (locally) homeomorphic to LF-spaces

“…In particular, each infinite-dimensional separable LF-space is homeomorphic to one of the following spaces: l 2 , R ∞ or l 2 × R ∞ . The topological characterizations of the LF-spaces l 2 and R ∞ were given by Toruńczyk [28], [29] and Sakai [25], respectively. Other LF-spaces were recently characterized by Banakh and Repovš [5].…”

Each 𝑅^{∞}-manifold has a unique piecewise linear 𝑅^{∞}-structure

“…The proof of the theorem proceeds in the spirit of [4]. In order to use the general position arguments (e.g.…”

“…Aspects of R°°-manifolds have been studied by R. E. Heisey, V. T. Liem, et al Their works show that the behavior of R00-manifolds is similar to that of /2-manifolds or Q-manifolds (cf. references of [4]). …”

“…[4]), each R00-manifold can be embedded as an open subset of R°°. Since open subsets of R°° have the p.l.…”