topology

plural topologies

1. uncountablemathematicsThe 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).

   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.

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   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.

   Synonyms: analysis situs, geometria situs

2. countableuncountablemathematicsAny 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.

   The subsets of a set X which constitute a topology are called the open sets of X.

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   A set X equipped with a topology #92;tau is called a topological space and denoted (X,#92;tau).

   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.

   2016, Ehud Hrushovski, François Loeser, Non-Archimedean Tame Topology and Stably Dominated Types (AM-192), Princeton University Press, page 43

3. countableuncountablemedicineThe anatomical structure of part of the body.
4. countableuncountablecomputingThe arrangement of nodes in a communications network.
5. countableuncountableengineeringThe properties of a particular technological embodiment that are not affected by differences in the physical layout or form of its application.
6. countableuncountablegeographyThe topographical study of geographic locations or given places in relation to their history.
7. countabledateduncountableThe art of, or method for, assisting the memory by associating the thing or subject to be remembered with some place.