- point-set topology
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The general field of topology, not restricting attention to specific classes of spaces, and not using algebraic topology.
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point-set topology
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point set topology — noun : a branch of topology concerned with the properties and theory of topological spaces and metric spaces developed with emphasis on set theory * * * Math. topology (def. 2). [1955 60] … Useful english dictionary
point set topology — noun Date: 1957 a branch of topology concerned with the properties and theory of topological spaces and metric spaces developed with emphasis on set theory … New Collegiate Dictionary
point set topology — Math. topology (def. 2). [1955 60] * * * … Universalium
point set — noun : a collection of points in geometry or topology * * * point set noun (mathematics) An aggregate • • • Main Entry: ↑point * * * n. (in acupuncture) a set of points stimulated simultaneously to treat a particular ailment or bring about a… … Useful english dictionary
Topology — (Greek topos , place, and logos , study ) is the branch of mathematics that studies the properties of a space that are preserved under continuous deformations. Topology grew out of geometry, but unlike geometry, topology is not concerned with… … Wikipedia
topology — topologic /top euh loj ik/, topological, adj. topologically, adv. topologist, n. /teuh pol euh jee/, n., pl. topologies for 3. Math. 1. the study of those properties of geometric forms that remain invariant under c … Universalium
Point (geometry) — In geometry, topology and related branches of mathematics a spatial point describes a specific point within a given space that consists of neither volume, area, length, nor any other higher dimensional analogue. Thus, a point is a 0 dimensional… … Wikipedia
Open set — Example: The points (x, y) satisfying x2 + y2 = r2 are colored blue. The points (x, y) satisfying x2 + y2 < r2 are colored red. The red points form an open set. The blue points form a closed set. The union of the red and blue points is a… … Wikipedia
Pointless topology — In mathematics, pointless topology (also called point free or pointfree topology) is an approach to topology which avoids the mentioning of points. General conceptsTraditionally, a topological space consists of a set of points, together with a… … Wikipedia
Derived set (mathematics) — In mathematics, more specifically in point set topology, the derived set of a subset S of a topological space is the set of all limit points of S. It is usually denoted by S′. The concept was first introduced by Georg Cantor in 1872 and he… … Wikipedia
