topology
/təˈpɑləd͡ʒi/
Frequency: Zipf frequency 3.20 in modern English
Meaning
noun
The branch of mathematics dealing with those properties of a geometrical object (of arbitrary dimensionality) that are unchanged by continuous deformations (such as stretching, bending, etc., without tearing or gluing).
Uncountable
noun
Any collection τ of subsets of a given set X that contains both the empty set and X, and which is closed under finitary intersections and arbitrary unions.
Countable; Uncountable
noun
The properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
Countable; Uncountable
noun
The topographical study of geographic locations or given places in relation to their history.
Countable; Uncountable
noun
The art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.
Countable; Dated; Uncountable
Example Sentences
- "1970 [Addison-Wesley], Stephen Willard, General Topology, 2012, Dover, page v, This book is designed to develop the fundamental concepts of general topology which are the basic tools of working mathematicians in a variety of fields."
- "1974 [Crane, Russak & Co.], H. Graham Flegg, From Geometry to Topology, 2001, Dover, page v, Many university courses in topology plunge immediately into a formalized and entirely abstract presentation of topological concepts."
- "A set X equipped with a topology #92;tau is called a topological space and denoted (X,#92;tau)."
- "The subsets of a set X which constitute a topology are called the open sets of X."
- "It is easy to verify that the topology generated by these basic open sets coincides with the definition of the topology on #92;widehat#123;V#125; above, for the Zariski topology and the sheaf of functions #92;operatorname#123;val#125;(f),f regular."
Etymology
Word Breakdown
- Root: topologia
Regional Pronunciation
- American English: /təˈpɑləd͡ʒi/
- British English: /təˈpɒləd͡ʒi/