Characterizations of (R∞,σ) - or (Q∞,Σ) -manifolds and their applications

✍ Scribed by Taras Banakh; Katsuro Sakai

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 181 KB
• Volume: 106
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(99)00081-4

✦ Synopsis

We identify Euclidean spaces R n with the subspaces of the countable infinite product R ω . Then the set n∈N R n has two natural topologies, namely the weak topology (the direct limit) with respect to the tower R 1 ⊂ R 2 ⊂ R 3 ⊂ • • • and the relative topology inherited from the product topology of R ω . We denote these spaces by R ∞ and σ , respectively. Thus the bitopological space (R ∞ , σ ) is obtained. Replacing R with the Hilbert cube Q = [-1, 1] ω , we can define the bitopological space (Q ∞ , Σ). In this paper, we give several characterizations of the bitopological manifolds modeled on (R ∞ , σ ) or (Q ∞ , Σ), which are applied to bitopological groups, bitopological linear spaces, spaces of measures, spaces of maps, hyperspaces, etc.