Topology began with the analysis of assertive questions in geometry. Leonhard Euler's 1736 cardboard on the Seven Bridges of Königsberg1 is admired as one of the aboriginal bookish treatises in avant-garde topology.
The appellation "Topologie" was alien in German in 1847 by Johann Benedict Listing in Vorstudien zur Topologie,2 who had acclimated the chat for ten years in accord afore its aboriginal actualization in print. "Topology," its English form, was aboriginal acclimated in 1883 in Listing's obituary in the account Nature3 to analyze "qualitative geometry from the accustomed geometry in which quantitative relations chiefly are treated". The appellation topologist in the faculty of a specialist in cartography was acclimated in 1905 in the annual Spectator.citation needed However, none of these uses corresponds absolutely to the avant-garde analogue of topology.
Modern cartography depends acerb on the account of set theory, developed by Georg Cantor in the after allotment of the 19th century. Cantor, in accession to establishing the basal account of set theory, advised point sets in Euclidean amplitude as allotment of his abstraction of Fourier series.
Henri Poincaré appear Analysis Situs in 1895,4 introducing the concepts of homotopy and homology, which are now advised allotment of algebraic topology.
Maurice Fréchet, accumulation the assignment on action spaces of Cantor, Volterra, Arzelà, Hadamard, Ascoli, and others, alien the metric amplitude in 1906.5 A metric amplitude is now advised a appropriate case of a accepted topological space. In 1914, Felix Hausdorff coined the appellation "topological space" and gave the analogue for what is now alleged a Hausdorff space.6 In accepted usage, a topological amplitude is a slight generalization of Hausdorff spaces, accustomed in 1922 by Kazimierz Kuratowski.citation needed
For added developments, see point-set cartography and algebraic topology.
The appellation "Topologie" was alien in German in 1847 by Johann Benedict Listing in Vorstudien zur Topologie,2 who had acclimated the chat for ten years in accord afore its aboriginal actualization in print. "Topology," its English form, was aboriginal acclimated in 1883 in Listing's obituary in the account Nature3 to analyze "qualitative geometry from the accustomed geometry in which quantitative relations chiefly are treated". The appellation topologist in the faculty of a specialist in cartography was acclimated in 1905 in the annual Spectator.citation needed However, none of these uses corresponds absolutely to the avant-garde analogue of topology.
Modern cartography depends acerb on the account of set theory, developed by Georg Cantor in the after allotment of the 19th century. Cantor, in accession to establishing the basal account of set theory, advised point sets in Euclidean amplitude as allotment of his abstraction of Fourier series.
Henri Poincaré appear Analysis Situs in 1895,4 introducing the concepts of homotopy and homology, which are now advised allotment of algebraic topology.
Maurice Fréchet, accumulation the assignment on action spaces of Cantor, Volterra, Arzelà, Hadamard, Ascoli, and others, alien the metric amplitude in 1906.5 A metric amplitude is now advised a appropriate case of a accepted topological space. In 1914, Felix Hausdorff coined the appellation "topological space" and gave the analogue for what is now alleged a Hausdorff space.6 In accepted usage, a topological amplitude is a slight generalization of Hausdorff spaces, accustomed in 1922 by Kazimierz Kuratowski.citation needed
For added developments, see point-set cartography and algebraic topology.
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