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Brief History of Algebraic Topology: Motivation of the Subject and Historical Development

In: Basic Topology 3

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  • Mahima Ranjan Adhikari

    (Institute for Mathematics, Bioinformatics, Information Technology and Computer Science (IMBIC))

Abstract

This chapter conveys the history of emergence of the concepts leading to the development of algebraic topology as a subject with their motivations. Just after the concept of homeomorphisms is clearly defined, the subject of topology begins to study those properties of geometric figures which are preserved by homeomorphisms with an eye to classify topological spaces up to homeomorphism, which stands the ultimate problem in topology, where a geometric figure is considered to be a point set in the Euclidean space $$ \textbf{R}^n.$$ R n . But this undertaking becomes hopeless, when there exists no homeomorphism between the two given topological spaces.

Suggested Citation

  • Mahima Ranjan Adhikari, 2022. "Brief History of Algebraic Topology: Motivation of the Subject and Historical Development," Springer Books, in: Basic Topology 3, chapter 0, pages 449-468, Springer.
    • Handle: RePEc:spr:sprchp:978-981-16-6550-9_7
    DOI: 10.1007/978-981-16-6550-9_7
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