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To define limits for real or complex sequences we used the absolute value to measure the distance between points. The same limit definitions can be applied to any set that is equipped with a suitable distance function. From the notion of distance we can derive a collection of interrelated concepts that includes limits, continuity, compactness, etc. These are the basic notions of topology, and the term metric topology Topology refers to the case where all of these concepts are derived from a distance function.

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Metric Topology

  • 章节

  • 发表日期：

    2025年

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  • David Borthwick

摘要

To define limits for real or complex sequences we used the absolute value to measure the distance between points. The same limit definitions can be applied to any set that is equipped with a suitable distance function. From the notion of distance we can derive a collection of interrelated concepts that includes limits, continuity, compactness, etc. These are the basic notions of topology, and the term metric topology Topology refers to the case where all of these concepts are derived from a distance function.