Topology | Wikipedia audio article
Channel: wikipedia tts
Date: 25/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Topology


00:01:24 1 History
00:04:21 2 Introduction
00:09:53 3 Concepts
00:10:02 3.1 Topologies on sets
00:11:32 3.2 Continuous functions and homeomorphisms
00:12:32 3.3 Manifolds
00:13:23 4 Topics
00:13:31 4.1 General topology
00:14:59 4.2 Algebraic topology
00:15:50 4.3 Differential topology
00:16:50 4.4 Geometric topology
00:18:23 4.5 Generalizations
00:18:55 5 Applications
00:19:04 5.1 Biology
00:19:54 5.2 Computer science
00:20:41 5.3 Physics
00:22:25 5.4 Geography and Landscape Ecology
00:22:56 5.5 Robotics
00:23:22 5.6 Games and puzzles
00:23:38 5.7 Fiber Art



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SUMMARY
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In mathematics, topology (from the Greek τόπος, place, and λόγος, study) is concerned with the properties of space that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing.
An n-dimensional topological space is a space (not necessarily Euclidean) with certain properties of connectedness and compactness.The space may be continuous (like all points on a rubber sheet), or discrete (like the set of integers). It can be open (like the set of points inside a circle) or closed (like the set of points inside a circle, together with the points on the circle).
Topology developed as a field of study out of geometry and set theory, through analysis of concepts such 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.