# 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.

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