A topological space is k-resolvable if X has k disjoint dense subsets. In this paper we shall give a new proof for ℵ0-resolvability of each metric space without ...
In this paper we shall give a new proof for ℵ0-resolvability of a metric space without an isolated point by using simple induction. It is worth noting that ...
A topological space is k-resolvable if X has k disjoint dense subsets. In this paper we shall give a new proof for N-0-resolvability of each metric space ...
Missing: ℵ0- | Show results with:ℵ0-
"A New Proof of ℵ0-Resolvability of a Metric Space Without an Isolated Point." The American Mathematical Monthly 122, no. 9 (2015): 897-898. Daneshpajouh ...
Jun 13, 2021 · I'm trying to prove this theorem: Let (X,d) be a complete metric space, with no isolated points, prove X is uncountable.
Missing: Resolvability | Show results with:Resolvability
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In this paper we shall give a new proof for ℵ0-resolvability of each metric space without an isolated point. ...read more read less. PDF. Save. Cite. Journal ...
A new proof of ℵ0−resolvability of a metric space without an isolated point, Amer. Math. Monthly (2015), DOI: 10.4169/amer.math.monthly.122.9.897 [abstract].
Jun 11, 2021 · To prove directly: Q×Q ≈ Q. Q∩(0,1] ≈ Q∩(0,1). A standard modern proof (Engelking 1995: exercises with hints). ▷ Any countable metric space ...
Missing: ℵ0- Resolvability
Oct 8, 2007 · Every Sκ-space is κ-resolvable. Proof: Let X = Jλ<κ Xλ be an Sκ-space. Of course, X does not have any isolated points.
We prove that, assuming MA, every crowded T 0 space X is ω-resolvable if it satisfies one of the following properties: (1) it contains a π-network of ...