Topology (nonfiction): Difference between revisions
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In [[Mathematics (nonfiction)|mathematics]], '''topology''' (from the Greek τόπος, ''place'', and λόγος, ''stud''y) is concerned with the properties of space that are preserved under continuous function deformations, such as stretching and bending, but not tearing or gluing. | [[File:Mug_and_Torus_morph.gif|thumb|A continuous deformation (a type of homeomorphism) of a mug into a doughnut (torus) and back.]]In [[Mathematics (nonfiction)|mathematics]], '''topology''' (from the Greek τόπος, ''place'', and λόγος, ''stud''y) is concerned with the properties of space that are preserved under continuous function deformations, such as stretching and bending, but not tearing or gluing. | ||
Topology can be studied by considering a collection of subsets, called [[Open set|open sets]], that satisfy certain properties, turning the given set into a topological space. | Topology can be studied by considering a collection of subsets, called [[Open set|open sets]], that satisfy certain properties, turning the given set into a topological space. | ||
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[[Leonhard Euler (nonfiction)|Leonhard Euler]]'s [[Seven Bridges of Königsberg Problem (nonfiction)|Seven Bridges of Königsberg Problem]] and [[Polyhedron Formula (nonfiction)|Polyhedron Formula]] are arguably the field's first theorems. | [[Leonhard Euler (nonfiction)|Leonhard Euler]]'s [[Seven Bridges of Königsberg Problem (nonfiction)|Seven Bridges of Königsberg Problem]] and [[Polyhedron Formula (nonfiction)|Polyhedron Formula]] are arguably the field's first theorems. | ||
The term ''topology'' was introduced by [[Johann Benedict Listing (nonfiction)|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. | The term ''topology'' was introduced by [[Johann Benedict Listing (nonfiction)|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 (nonfiction)|topological space]] was developed. | ||
By the middle of the 20th century, topology had become a major branch of [[Mathematics (nonfiction)|mathematics]]. | By the middle of the 20th century, topology had become a major branch of [[Mathematics (nonfiction)|mathematics]]. | ||
== In the News == | |||
<gallery> | |||
File:Topological space examples.png|link=Topological space (nonfiction)|[[Topological space (nonfiction)|Topological spaces]] charged as accessories to [[crimes against mathematical constants]]. | |||
</gallery> | |||
== Fiction cross-reference == | == Fiction cross-reference == | ||
* [[Gnomon algorithm]] | |||
* [[Mathematics]] | |||
* [[Reidemeister move]] | |||
== Nonfiction cross-reference == | == Nonfiction cross-reference == | ||
* In topology, an Akbulut cork is a structure that is frequently used to show that in four dimensions, the smooth h-cobordism theorem fails. It was named after Turkish mathematician Selman Akbulut. https://en.wikipedia.org/wiki/Akbulut_cork | |||
* [[Geometry (nonfiction)]] | * [[Geometry (nonfiction)]] | ||
* [[Gottfried Leibniz (nonfiction) | * [[Gottfried Leibniz (nonfiction)]] | ||
* [[Leonhard Euler (nonfiction) | * [[Leonhard Euler (nonfiction)]] | ||
* [[Manifold (nonfiction)]] | |||
* [[Mathematics (fiction)]] | * [[Mathematics (fiction)]] | ||
* [[Reidemeister move (nonfiction)]] | |||
* [[Topological graph theory (nonfiction)]] | |||
* [[Topological space (nonfiction)]] | |||
* [[Torus (nonfiction)]] | |||
External links: | External links: | ||
Latest revision as of 04:55, 27 February 2019
In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous function deformations, such as stretching and bending, but not tearing or gluing.
Topology can be studied by considering a collection of subsets, called open sets, that satisfy certain properties, turning the given set into a topological space.
Important topological properties include connectedness and Compact space.
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 Gottfried Leibniz, who in the 17th century envisioned the geometria situs (Greek-Latin for "geometry of place") and analysis situs (Greek-Latin for "picking apart of place").
Leonhard Euler's Seven Bridges of Königsberg Problem and Polyhedron Formula are arguably the field's first theorems.
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.
In the News
Topological spaces charged as accessories to crimes against mathematical constants.
Fiction cross-reference
Nonfiction cross-reference
- In topology, an Akbulut cork is a structure that is frequently used to show that in four dimensions, the smooth h-cobordism theorem fails. It was named after Turkish mathematician Selman Akbulut. https://en.wikipedia.org/wiki/Akbulut_cork
- Geometry (nonfiction)
- Gottfried Leibniz (nonfiction)
- Leonhard Euler (nonfiction)
- Manifold (nonfiction)
- Mathematics (fiction)
- Reidemeister move (nonfiction)
- Topological graph theory (nonfiction)
- Topological space (nonfiction)
- Torus (nonfiction)
External links:
- Topology @ Wikipedia