topological space In A Sentence

Learn how to use topological space in a sentence and make better sentences with `topological space` by reading topological space sentence examples.

• A topological space is locally metrizable Hausdorff space.
• After this identification, we arrive at a topological space homeomorphic to the rotation group.
• The method herein used is of creativeness. The conclusion reached is also of real plenitude to the theoretical basis about topological space.
• A topological space is said to be disjoint subsets have disjoint compact closures.
• In this note two generality theorems on topological space theory are established, they improve several theorems of Gao Guoshi.
• There are several inequivalent definitions of Baire sets, so correspondingly there are several inequivalent concepts of Baire measure on a topological space.
• Topological indistinguishability defines an equivalence relation on any topological space " X ".
• Every metric space is therefore, in a natural way, a topological space.
• A topological space " X " is submaximal if and only if every dense subset is open.
• A topological space is preregular if and only if its Kolmogorov quotient is Hausdorff.
• Schemata are a special case of cylinder sets, and hence form a topological space.
• Based on several examples, this paper introduces several kinds of particular topological space construction, which brought a series of conclusion.
• Structure must definitely include topological space as well as the standard abstract algebra notions.
• The concept of -generalized convex set-valued map is defined in linear topological space.
• Where the discrete topology is initial or free, the indiscrete topology is final or cofree : every function " from " a topological space " to " an indiscrete space is continuous, etc.
• A square is a contractible topological space, which implies that it has trivial homology.
• It is supposed to illustrate how a topological space can be associated with a vector space.
• Through discussing the separation axiom of topological space, we can get the relation - chain of separation axioms.
• Under meager point-set hypotheses, namely indiscrete topological space show that not all topological spaces can be expressed using Grothendieck topologies.
• There are, however, some subtleties to consider when dealing with general distributions defined on a sigma algebra, rather than on a topological space.
• As a topological space, the real numbers are separable.
• The density of a topological space is a topological invariant.
• An equivalent formulation is : If " X " is a compact Hausdorff topological space which satisfies the ccc then " X " is not the union of "'k "'or fewer nowhere dense subsets.
• This paper not only gives a kind of topological space with path connected base, i.
• The relation of being homotopic is an equivalence relation on paths in a topological space.
• An arbitrary union of open sets in a topological space is open.
• The structure of a topological space may be defined as an closed set topology.
• Some new generalized L-KKM type theorems are proves in a topological space with property(H), furthermore, matching theorems with open cover are obtained.
• A set with a topology is called a " topological space ".
• This definition of weak convergence can be extended for " S " any metrizable topological space.
• Even more generally, one can study sequences with elements in some topological space.
• This work concentrated on the domain is a given topological space.
• Let X be a topological space, and f colon X to X a homeomorphism.
• If space time is the space of all possible connections of the-bundle is homotopically equivalent to the topological sphere.
• These spaces are quasi-compact, quasi-separated, and functorial in the rigid space, but lack a lot of nice topological properties.
• In this paper, the Cartesian Product of three topological spaces, compact space, connected space and A2(A1) space, were studied(sentence dictionary), and three corresponding conclusions are given.
• The topological relationship of nodes and road sections in road network was expressed by adjacent node relation matrix and adjacent node weight matrix, which saved the storage space.
• By using a universal method a new existence theorem of solution for a generalized equilibrium problem in topological vector space is obtained.
• The is a discrete space, and the a topological graph.
• The topological structure of the decision space can be quite complicated in even a fairly simple program.
• This implies e . g . that every completely metrizable topological vector space is complete.
• In this paper the saddle point of function in topological linear space is discussed. The results given which functional exists saddle point are helpful to the theory of games.
• Namely, if a topological vector space is finite dimensional, it is locally compact.
• The generation employs space filling curves to preserve the spatial and topological properties (see the Resources section for the H. Sagan book).
• We introduce the notion of topological direct sum, and get a representative theorem of inductive limit by topological direct sum and quotient space.
• Alaoglu's theorem states that if " E " is a topological vector space, then every equicontinuous subset of " E * " is weak-* relatively compact.