### Examples

- The "objects" of topology are often formally defined as topological spaces. A set for which a topology has been specified is called a topological space (Munkres 2000, p. 76). —
*“Topology -- from Wolfram MathWorld”*, - In mathematics, a topological space is an ordered pair where is a set and is a certain collection of subsets of called the open sets or the topology of. A topological space is an ordered pair where is a set and is a collection of subsets of (i.e., any element is. —
*“Topological space - encyclopedia article - Citizendium”*, - Definition of topological in the Online Dictionary. Meaning of topological. Pronunciation of topological. Translations of topological. topological synonyms, topological antonyms. Information about topological in the free online English. —
*“topological - definition of topological by the Free Online”*, - topological (not comparable) (mathematics) of or relating to topology [edit] Derived topological space [edit] Translations. of or relating to topology. —
*“topological - Wiktionary”*, - (3) G-automorphic, if X is a topological group and each translation systematically appear in many trends of Topological Algebra and Topological Dy. —
*“TOPOLOGICAL TRANSFORMATION GROUPS: SELECTED TOPICS”*, u.cs.biu.ac.il - Ideas that are now classified as topological were expressed as early as 1736. In 1914, Felix Hausdorff coined the term "topological space" and gave the definition for what is now called a Hausdorff space.[6] In current usage, a topological space is a slight generalization of Hausdorff. —
*“Topology - Wikipedia, the free encyclopedia”*, - We show how this can be used to extend (co)homology. theories to topological stacks. The category of topological stacks accommodates various classes of objects si. —
*“HOMOTOPY TYPES OF TOPOLOGICAL STACKS”*, math.fsu.edu - In mathematics, topology is a branch concerned with the study of topological spaces. Topology is also concerned with the study of the so-called topological properties of figures, that is to say properties that do not change under bicontinuous one-to-one transformations (called homeomorphisms). —
*“Topology - Wikinfo”*, - a topological space may be restated as follows: A family of subsets T ) be a topological space and let A X. A point x in X is. a limit point of A if every. —
*“Chapter 3 Topological Spaces”*, education.uncc.edu - Likewise, the concept of a topological space is concerned with generalizing the structure of sets in Euclidean spaces. In fact, there are many equivalent ways to define what we will call a topological space just by defining families of subsets of a given set. —
*“Topology/Topological Spaces - Wikibooks, collection of open”*, - topological groups ( ¦täpə¦läjəkəl ′grüps ) ( mathematics ) Groups which also have a topology with the property that the group operation. —
*“Topological group: Definition from ”*, - Entirely ***ogously, one can define topological left and right vector spaces over a (not necessarily commutative) topological division ring. Two topological vector spaces and over the same topological field are said to be. —
*“Springer Online Reference Works”*, - We deﬁne the action of a locally compact group G on a topological of a topological graph E by a. locally compact group G via a cocycle c : E. 1. G. If G is. —
*“Group actions on topological graphs”*, wolfweb.unr.edu - Buy topological, Books items on eBay. Find great deals on Business Industrial, Collectibles items and get what you want now!. —
*“topological items - Get great deals on Books, Business”*, - Topological definition, the study of those properties of geometric forms that remain invariant under certain transformations, as bending or stretching. See more. —
*“Topological | Define Topological at ”*, - We study (countably) compact and (absolutely) -closed primitive topological inverse semigroups. We describe the structure of compact and countably compact primitive topological inverse semigroups and show that any countably compact primitive. —
*“Brandt Extensions and Primitive Topological Inverse Semigroups”*, - Topological spaces are structures that allow one to formalize concepts such as convergence, connectedness and continuity. They appear in all branches of modern mathematics and can be seen as a central unifying notion. Formally, a topological space is a set X together with a collection T. —
*“Encyclopedia4U - Topological space - Encyclopedia Article”*, encyclopedia4 - Topological Data ***ysis. The title is about a recent mathematical method to ***yze. data Topological Data ***ysis. The title is about a recent mathematical method to ***yze. data. —
*“Topological Data ***ysis”*, piedmont.edu - Figure 1: Topological entropy generated in a so-called horseshoe: the rectangle is stretched, bent upward and placed over itself. The number of orbits distinguishable in steps grows as , generating the topological entropy. —
*“Topological entropy - Scholarpedia”*, - X and Y is again a topological stack if Y admits a groupoid presentation [Y X and Y be topological stacks. The purpose of these notes is to show. —
*“MAPPING STACKS OF TOPOLOGICAL STACKS”*,