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In 1936, Franz habilited in the field of algebraic topology under Kurt Reidemeister in Marburg. In 1937 he moved to the University of Giessen, where he taught as a lecturer from 1939 onwards. Franz wanted to change to Frankfurt in 1940, but in the summer of 1940 he was promoted to the command post of the Wehrmacht.
Kelley's 1955 text, General Topology, which eventually appeared in three editions and several translations, is a classic and widely cited graduate-level introduction to topology. An appendix sets out a new approach to axiomatic set theory, now called Morse–Kelley set theory, that builds on Von Neumann–Bernays–Gödel set theory.
In mathematics, general topology (or point set topology) is the branch of topology that deals with the basic set-theoretic definitions and constructions used in topology. It is the foundation of most other branches of topology, including differential topology , geometric topology , and algebraic topology .
The Stone–Čech compactification of the topological space X is a compact Hausdorff space βX together with a continuous map i X : X → βX that has the following universal property: any continuous map f : X → K, where K is a compact Hausdorff space, extends uniquely to a continuous map βf : βX → K, i.e. (βf)i X = f.
Module theory and general chain complexes are developed by Noether and her students, and algebraic topology begins as an axiomatic approach grounded in abstract algebra. 1931: Georges de Rham: De Rham's theorem: for a compact differential manifold, the chain complex of differential forms computes the real (co)homology groups. [26] 1931: Heinz Hopf
Categorical topology: The study of topological categories of structured sets (generalizations of topological spaces, uniform spaces and the various other spaces in topology) and relations between them, culminating in universal topology. General categorical topology study and uses structured sets in a topological category as general topology ...
In mathematics, general topology or point set topology is that branch of topology which studies properties of general topological spaces (which may not have further structure; for example, they may not be manifolds), and structures defined on them.
Allen Hatcher, Algebraic Topology, Cambridge University Press, Cambridge, 2002. ISBN 0-521-79540-0. A modern, geometrically flavored introduction to algebraic topology. The book is available free in PDF and PostScript formats on the author's homepage. Kainen, P. C. (1971). "Weak Adjoint Functors". Mathematische Zeitschrift. 122: 1– 9.