2022/02/17 by Katsuhisa Koshino, Koshino, Katsuhisa
Mathematics · #54E35 #54E40 #54E45 #Advanced Banach Space Theory #Advanced Topology and Set Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #General Topology (math.GN) #Primary: 54C35 #Secondary: 57N20
paper · pdf · doi:10.48550/arxiv.2202.08615
openalex publication_date 2022/02/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a separable locally compact but not compact metrizable space X, let αX = X ∪ \x_∞\ be the one-point compactification with the point at infinity x_∞. We denote by EM(X) the space consisting of admissible metrics on X, which can be extended to an admissible metric on αX, endowed with the compact-open topology. Let c0 ⊂ (0,1)^ℕ be the space of sequences converging to 0. In this paper, we shall show that if X is separable, locally connected and locally compact but not compact, and there exists a sequence \Ci\ of connected sets in X such that for all positive integers i, j ∈ ℕ with |i - j| ≤ 1, Ci ∩ Cj ≠ ∅, and for each compact set K ⊂ X, there is a positive integer i(K) ∈ ℕ such that for any i ≥ i(K), Ci ⊂ X ∖ K, then EM(X) is homeomorphic to c0.