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1. Metric space is a specific topological space, and it is an important process to understand topological space.

2. This paper not only gives a kind of topological space with path connected base, i.

3. There is a simple way of associating a topological space with a graph.

4. It proved that extended topological space is compactification space of topological space added to two points.

5. Since both general topological space and fuzzy topological space are special cases of topological molecule lattice, these results can be widely used.

6. In this paper, some topological space with transmissibility and some topological space without transmissibility in set-topology are discussed by enumerating some examples.

7. In the first chapter, the formation of topological space theory is simply introduced, as well as some knowledge about covering property and hyperspaces.

8. This paper studies the covering dimension of fuzzy topological space, discusses the relationship between general covering dimension and fuzzy covering dimension.

9. There exists a counterexample showing that a compact topological space is not necessarily a sequentially compact space.

10. This paper not only gives a kind of topological space with path connected base, i. e. local path connected space, but also gives its topological structure and its topological property.

11. In this note two generality theorems on topological space theory are established, they improve several theorems of Gao Guoshi.

12. Through discussing the separation axiom of topological space, we can get the relation - chain of separation axioms.

13. Minimax theorem in a general topological space is obtained. Moreover, a saddle point theorem on a topological space without any linear structure is established.

13. Sentencedict.com is a sentence dictionary, on which you can find good sentences for a large number of words.

14. In this paper, concepts of Pre-semiopen sets, Sub-strong semiopen sets and Strong semiopen sets were introduced in topological space in a new way, and their relations and properties were discussed.

15. In this paper the application of homotopy equivalence transformation of topological space sets to the topological classification of states and defects in ordered media is discussed.

16. Some new generalized L-KKM type theorems are proves in a topological space with property(H), furthermore, matching theorems with open cover are obtained.

17. Based on the nonstandard topology definition and enlarged model, the concept of compactness in the topological space are described and characterized in this paper.

18. The method herein used is of creativeness. The conclusion reached is also of real plenitude to the theoretical basis about topological space.

19. Secondly, in order to favor utilizing this theorem, several propositions are given on the homotopy equivalence between two topological space sets.

20. Aim To study the existence of the extreme points of a compact set in linear topological space.

21. This paper discusses the relationship between quasi-concave and pseudo-convex in the generalized convex function in the Linear topological space and offers some conditions of equivalence.

22. The concept of -generalized convex set-valued map is defined in linear topological space.

23. Based on several examples, this paper introduces several kinds of particular topological space construction, which brought a series of conclusion.

24. It has been proved that the nature of independence exists in the axiomatic system of Group, Euclidean space, distance space and topological space.