A convergence not metrizable

Fuente: arXiv
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Main Author: Rivera, Luis David
Format: Preprint
Published: 2024
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_version_ 1866914208505921536
author Rivera, Luis David
author_facet Rivera, Luis David
contents Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies involved are metrizable, which in an advantage since there is an extensive theory on convergence in metric spaces. However, the case of pointwise convergence is delicate, since it is shown that under certain hypotheses this form of convergence of sequences of functions is not equivalent to convergence in metric.
format Preprint
id arxiv_https___arxiv_org_abs_2410_12792
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle A convergence not metrizable
Rivera, Luis David
General Mathematics
54A20, 40A30
Certain notions of convergence of sequences functions such as pointwise convergence and (uniform) convergence on compact or bounded sets come from suitable topological function spaces; see [1]. Under certain conditions these topologies involved are metrizable, which in an advantage since there is an extensive theory on convergence in metric spaces. However, the case of pointwise convergence is delicate, since it is shown that under certain hypotheses this form of convergence of sequences of functions is not equivalent to convergence in metric.
title A convergence not metrizable
topic General Mathematics
54A20, 40A30
url https://arxiv.org/abs/2410.12792