The notion of connectedness in mathematical analysis of XIX century
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RIS BIB ENDNOTEThe notion of connectedness in mathematical analysis of XIX century
Publication date: 19.09.2014
Technical Transactions, 2014, Fundamental Sciences Issue 1 NP (7) 2014, pp. 195-209
https://doi.org/10.4467/2353737XCT.14.071.2521Authors
The notion of connectedness in mathematical analysis of XIX century
The notion of connectedness was introduced by Listing in 1847 and was further developed by Riemann, Jordan and Poincaré. The notion and rigorous definition of metric and topological space were formed in Frechet’s works in 1906, and in Hausdorff’s works in 1914. The notion of continuum could be traced back to antiquity, but its mathematical definition was formed in XIX century, in the works of Cantor and Dedekind, later of Hausdorff and Riesz. Karl Weierstrass (1815–1897) brought mathematical analysis to a rigorous form; also, the notions of future areas of mathematics – functional analysis and topology – were formed in his reasoning. Weierstrass’s works were not translated into Russian, and his lectures were not published even in Germany. In 1989, synopses of his lectures devoted to additional chapters of the theory of functions were published. Their material served as the basis for this article.
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Information: Technical Transactions, 2014, Fundamental Sciences Issue 1 NP (7) 2014, pp. 195-209
Article type: Original article
Titles:
The notion of connectedness in mathematical analysis of XIX century
The notion of connectedness in mathematical analysis of XIX century
Department of Mathematics, St. Petersburg State University of Architecture and Civil Engineering, St. Petersburg, Russia
Published at: 19.09.2014
Article status: Open
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