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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 ...
In topology and related fields of mathematics, there are several restrictions that one often makes on the kinds of topological spaces that one wishes to consider. Some of these restrictions are given by the separation axioms. These are sometimes called Tychonoff separation axioms, after Andrey Tychonoff.
Download as PDF; Printable version ... ) is a Lie group with respect to the topology of uniform convergence on ... Foundations and construction principles ...
In mathematics, Lehrbuch der Topologie (German for "textbook of topology") is a book by Herbert Seifert and William Threlfall, first published in 1934 and published in an English translation in 1980. It was one of the earliest textbooks on algebraic topology, and was the standard reference on this topic for many years. Albert W. Tucker wrote a ...
Print/export Download as PDF; ... the overlapping interval topology is a topology which is used to illustrate various topological principles.
Print/export Download as PDF; Printable version; In other projects Wikimedia Commons; ... Triangulation (topology) This page was last ...
The product topology on is equal to the initial topology induced by the canonical projections : as ranges over . [4] Consequently, the initial topology on induced by {:} is equal to the inverse image of the product topology on by the evaluation map:. [4] Furthermore, if the maps {} separate points on then the evaluation map is a homeomorphism ...
Cauchy space – Concept in general topology and analysis; Convergence space – Generalization of the notion of convergence that is found in general topology; Filters in topology – Use of filters to describe and characterize all basic topological notions and results. Sequential space – Topological space characterized by sequences