- open-interval topology
- мат. топология открытых интервалов
Большой англо-русский и русско-английский словарь. 2001.
open-interval topology
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Nested interval topology — In mathematics, more specifically general topology, the nested interval topology is an example of a topology given to the open interval (0,1), i.e. the set of all real numbers x such that 0 < x < 1. The open interval (0,1) is the set of all … Wikipedia
Overlapping interval topology — Not to be confused with Interlocking interval topology. In mathematics, the overlapping interval topology is a topology which is used to illustrate various topological principles. Definition Given the closed interval [ − 1,1] of the real number… … Wikipedia
Interval (mathematics) — This article is about intervals of real numbers. For intervals in general mathematics, see Partially ordered set. For other uses, see Interval. In mathematics, a (real) interval is a set of real numbers with the property that any number that lies … Wikipedia
Open and closed maps — In topology, an open map is a function between two topological spaces which maps open sets to open sets.[1] That is, a function f : X → Y is open if for any open set U in X, the image f(U) is open in Y. Likewise, a closed map is a function… … Wikipedia
Counterexamples in Topology — Author(s) Lynn Arthur Steen J. Ar … Wikipedia
Lower limit topology — In mathematics, the lower limit topology or right half open interval topology is a topology defined on the set R of real numbers; it is different from the standard topology on R and has a number of interesting properties. It is the topology… … Wikipedia
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
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
Order topology — In mathematics, an order topology is a certain topology that can be defined on any totally ordered set. It is a natural generalization of the topology of the real numbers to arbitrary totally ordered sets. If X is a totally ordered set, the order … Wikipedia
Long line (topology) — In topology, the long line (or Alexandroff line) is a topological space analogous to the real line, but much longer. Because it behaves locally just like the real line, but has different large scale properties, it serves as one of the basic… … Wikipedia
Base (topology) — In mathematics, a base (or basis) B for a topological space X with topology T is a collection of open sets in T such that every open set in T can be written as a union of elements of B. We say that the base generates the topology T. Bases are… … Wikipedia
