Every metric space of weight λ=λ?0 admits a condensation onto a Banach space

Osipov A.V.; Pytkeev E.G.

首页> 外文期刊>Topology and its applications >Every metric space of weight λ=λ?0 admits a condensation onto a Banach space

【24h】

Every metric space of weight λ=λ?0 admits a condensation onto a Banach space

机译：Every metric space of weight λ=λ?0 admits a condensation onto a Banach space

获取原文

获取原文并翻译 | 示例

掌桥外文数据库（机构版） >>

开具论文收录证明 >>

文献代查 >>

页面导航

摘要
著录项
相关主题

摘要

? 2023 Elsevier B.V.In this paper, we have proved that for each cardinal number λ such that λ=λ?0 a metric space of weight λ admits a bijective continuous mapping onto a Banach space of weight λ. Then, we get that every metric space of weight continuum admits a bijective continuous mapping onto the Hilbert cube. This resolves the famous Banach's Problem (when does a metric (possibly Banach) space X admit a bijective continuous mapping onto a compact metric space?) in the class of metric spaces of weight continuum. Also we get that every metric space of weight λ=λ?0 admits a bijective continuous mapping onto a Hausdorff compact space. This resolves the Alexandroff Problem (when does a Hausdorff space X admit a bijective continuous mapping onto a Hausdorff compact space?) in the class of metric spaces of weight λ=λ?0.

著录项

来源
《Topology and its applications》 |2023年第1期|108486.1-108486.7|共7页
作者
Osipov A.V.; Pytkeev E.G.;
展开▼
作者单位

Krasovskii Institute of Mathematics and Mechanics Ural Federal University;

Krasovskii Institute of Mathematics and Mechanics;

展开▼
收录信息
原文格式 PDF
正文语种英语
中图分类
关键词
Alexandroff problem; Banach problem; Banach space; Compact metric space; Condensation; Hilbert cube;

Every metric space of weight λ=λ?0 admits a condensation onto a Banach space

摘要

著录项

相关主题

期刊订阅