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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 .
A three-dimensional model of a figure-eight knot.The figure-eight knot is a prime knot and has an Alexander–Briggs notation of 4 1.. Topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is the branch of mathematics concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling ...
Wolfgang Franz (born 4 October 1905 in Magdeburg, Germany; died 26 April 1996 [1]) was a German mathematician [2] [3] who specialised in topology particularly in 3-manifolds, which he generalized to higher dimensions. [4] He is known for the Reidemeister–Franz torsion. He also made important contributions to the theory of lens spaces.
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 ...
Grigori Perelman announced a proof of the full geometrization conjecture in 2003 using Ricci flow with surgery in two papers posted at the arxiv.org preprint server. Perelman's papers were studied by several independent groups that produced books and online manuscripts filling in the complete details of his arguments.
Continuum (topology) Extended real number line; Long line (topology) Sierpinski space; Cantor set, Cantor space, Cantor cube; Space-filling curve; Topologist's sine curve; Uniform norm; Weak topology; Strong topology; Hilbert cube; Lower limit topology; Sorgenfrey plane; Real tree; Compact-open topology; Zariski topology; Kuratowski closure ...
His research, comprising over 200 published papers, covers various subfields of general topology. He has done particularly important work in metrizability theory and generalized metric spaces , cardinal functions , topological function spaces and other topological groups , and special classes of topological maps.