Some new characterizations of metrizable spaces

2010 ◽  
Vol 47 (2) ◽  
pp. 223-229 ◽  
Author(s):  
Rongxin Shen
Keyword(s):  
Metrizable Spaces ◽  
Regular Networks

In this paper, some new metrization theorems about regular networks are obtained, which improve related results in [2], [10], [15], and [20].

Universal elements for families of separable metrizable spaces

1998 ◽  
Vol 91 (6) ◽  
pp. 3387-3415
Author(s):  
D. N. Georgiou ◽  
S. D. Iliadis
Keyword(s):  
Metrizable Spaces

scholarly journals Several results on compact metrizable spaces in $$\mathbf {ZF}$$

2021 ◽  
Author(s):  
Kyriakos Keremedis ◽  
Eleftherios Tachtsis ◽  
Eliza Wajch
Keyword(s):  
Continuum Hypothesis ◽  
Compact Spaces ◽  
Power Set ◽  
Compact Metrizable Space ◽  
Permutation Models ◽  
Independence Results ◽  
The Axiom Of Choice ◽  
Metrizable Spaces ◽  
Transfer Theorems ◽  
The Continuum

AbstractIn the absence of the axiom of choice, the set-theoretic status of many natural statements about metrizable compact spaces is investigated. Some of the statements are provable in $$\mathbf {ZF}$$ ZF , some are shown to be independent of $$\mathbf {ZF}$$ ZF . For independence results, distinct models of $$\mathbf {ZF}$$ ZF and permutation models of $$\mathbf {ZFA}$$ ZFA with transfer theorems of Pincus are applied. New symmetric models of $$\mathbf {ZF}$$ ZF are constructed in each of which the power set of $$\mathbb {R}$$ R is well-orderable, the Continuum Hypothesis is satisfied but a denumerable family of non-empty finite sets can fail to have a choice function, and a compact metrizable space need not be embeddable into the Tychonoff cube $$[0, 1]^{\mathbb {R}}$$ [ 0 , 1 ] R .

Optimal metrics on metrizable spaces

1971 ◽  
Vol 22 (1) ◽  
pp. 660-663
Author(s):  
Ludvik Janos
Keyword(s):  
Metrizable Spaces

Joint Distribution of Distances in Large Random Regular Networks

2013 ◽  
Vol 50 (03) ◽  
pp. 861-870 ◽  
Author(s):  
Justin Salez
Keyword(s):  
Joint Distribution ◽  
Marginal Distribution ◽  
Weak Sense ◽  
Regular Graphs ◽  
Random Array ◽  
Point To Point ◽  
Regular Networks ◽  
Different Sources ◽  
Individual Entry

We study the array of point-to-point distances in random regular graphs equipped with exponential edge lengths. We consider the regime where the degree is kept fixed while the number of vertices tends to ∞. The marginal distribution of an individual entry is now well understood, thanks to the work of Bhamidi, van der Hofstad and Hooghiemstra (2010). The purpose of this note is to show that the whole array, suitably recentered, converges in the weak sense to an explicit infinite random array. Our proof consists in analyzing the invasion of the network by several mutually exclusive flows emanating from different sources and propagating simultaneously along the edges.

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