What makes a space have large weight?

1994/01/11 by I. Juhász, István Juhász, Juhász, I. +5
Computer Science · Mathematics · #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #Mathematical and Theoretical Analysis #math.LO

paper · pdf · doi:10.48550/arxiv.math/9401203

arxiv created 1994/01/11 · openalex publication_date 1994/01/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We formulate several conditions (two of them are necessary and sufficient) which imply that a space of small character has large weight. In section 3 we construct a ZFC example of a first countable 0-dimensional space X of size 2^omega with w(X)=2^omega and nw(X)=omega, we show that CH implies the existence of a 0-dimensional space Y of size omega₁ with w(Y)=nw(Y)=omega₁ and chi(Y)=R(Y)=omega, and we prove that it is consistent that 2^omega is as large as you wish and there is a 0-dimensional space Z of size 2^omega such that w(Z)=nw(Z)=2^omega but chi(Z)=R(Z^omega)=omega.

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