Topology

Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with the study of topological spaces. When the discipline was first introduced it was called analysis situs (Latin analysis of place).

History

The root of topology was in the study of geometry in ancient cultures. Leonhard Euler's 1736 paper on Seven Bridges of Königsberg is regarded as one of the first results on geometry that does not depend on any measurements, i.e., one of the first topological results.

Related Topics:
Leonhard Euler - 1736 - Seven Bridges of Königsberg

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Georg Cantor, the inventor of set theory along with Gottlob Frege, had begun to study the theory of point sets in Euclidean space, in the later part of the 19th century.

Related Topics:
Georg Cantor - Set theory - Gottlob Frege - Euclidean space

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Henri Poincaré published Analysis Situs in 1895, introducing the concepts of homotopy and homology.

Related Topics:
Henri Poincaré - Homotopy - Homology

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Maurice Fréchet, unifying the work on function spaces of Cantor, Volterra, Arzelà, Hadamard, Ascoli and others, introduced the concept of metric space in 1906.

Related Topics:
Maurice Fréchet - Volterra - Arzelà - Hadamard - Metric space

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In 1914, Felix Hausdorff, generalizing the notion of metric space, coined the term "topological space" and gave the definition for what is now called Hausdorff space.

Related Topics:
Felix Hausdorff - Hausdorff space

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Finally, a further slight generalization in 1922, by Kazimierz Kuratowski, gives the present-day concept of topological space.

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The term "topologie" was introduced in German in 1847 by Johann Benedict Listing in Vorstudien zur Topologie, Vandenhoeck und Ruprecht, Göttingen, pp. 67, 1848. However, Listing had already used the word for ten years in correspondence. "Topology", its English form, was introduced in print by Solomon Lefschetz in 1930 to replace the earlier name "analysis situs". The separate status of the topologist, a specialist in topology, was probably established around 1920.

Related Topics:
Johann Benedict Listing - Solomon Lefschetz

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