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- Topology abstract "Topology (from the Greek τόπος, "place", and λόγος, "study") is the mathematical study of shapes and topological spaces. It is an area of mathematics concerned with the properties of space that are preserved under continuous deformations including stretching and bending, but not tearing or gluing. This includes such properties as connectedness, continuity and boundary.Topology developed as a field of study out of geometry and set theory, through analysis of such concepts as space, dimension, and transformation. Such ideas go back to Leibniz, who in the 17th century envisioned the geometria situs (Latin for "geometry of place") and analysis situs (Greek-Latin for "picking apart of place"). The term topology was introduced by Johann Benedict Listing in the 19th century, although it was not until the first decades of the 20th century that the idea of a topological space was developed. By the middle of the 20th century, topology had become a major branch of mathematics.Topology has many subfields:General topology establishes the foundational aspects of topology and investigates properties of topological spaces and investigates concepts inherent to topological spaces. It includes point-set topology, which is the foundational topology used in all other branches (including topics like compactness and connectedness).Algebraic topology tries to measure degrees of connectivity using algebraic constructs such as homology and homotopy groups.Differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.Geometric topology primarily studies manifolds and their embeddings (placements) in other manifolds. A particularly active area is low dimensional topology, which studies manifolds of four or fewer dimensions. This includes knot theory, the study of mathematical knots.See also: topology glossary for definitions of some of the terms used in topology, and topological space for a more technical treatment of the subject.".
- Topology thumbnail Möbius_strip.jpg?width=300.
- Topology wikiPageExternalLink 23.htm.
- Topology wikiPageExternalLink topology.
- Topology wikiPageExternalLink topgpds.html.
- Topology wikiPageExternalLink hmath1-whitney10.pdf.
- Topology wikiPageExternalLink zoo.
- Topology wikiPageExternalLink defs.txt.
- Topology wikiPageExternalLink index.html.
- Topology wikiPageID "29954".
- Topology wikiPageRevisionID "605587950".
- Topology hasPhotoCollection Topology.
- Topology id "p/t093200".
- Topology title "Topology, general".
- Topology subject Category:Mathematical_structures.
- Topology subject Category:Topology.
- Topology comment "Topology (from the Greek τόπος, "place", and λόγος, "study") is the mathematical study of shapes and topological spaces. It is an area of mathematics concerned with the properties of space that are preserved under continuous deformations including stretching and bending, but not tearing or gluing.".
- Topology label "Topologia (matemática)".
- Topology label "Topologia".
- Topology label "Topologia".
- Topology label "Topologie (Mathematik)".
- Topology label "Topologie".
- Topology label "Topologie".
- Topology label "Topology".
- Topology label "Topología".
- Topology label "Топология".
- Topology label "طوبولوجيا".
- Topology label "位相幾何学".
- Topology label "拓扑学".
- Topology sameAs Topologie.
- Topology sameAs Topologie_(Mathematik).
- Topology sameAs Τοπολογία.
- Topology sameAs Topología.
- Topology sameAs Topologia.
- Topology sameAs Topologie.
- Topology sameAs Topologi.
- Topology sameAs Topologia.
- Topology sameAs 位相幾何学.
- Topology sameAs 위상수학.
- Topology sameAs Topologie.
- Topology sameAs Topologia.
- Topology sameAs Topologia_(matemática).
- Topology sameAs m.07cj3.
- Topology sameAs Q42989.
- Topology sameAs Q42989.
- Topology wasDerivedFrom Topology?oldid=605587950.
- Topology depiction Möbius_strip.jpg.
- Topology isPrimaryTopicOf Topology.
