1. The Sierpiński space is the simplest non-discrete topological space.

2. Every real or complex affine or projective space is also a topological space.

3. We introduce the notion of topological direct sum, and get a representative theorem of inductive limit by topological direct sum and quotient space.

4. In order to turn a topological space into a measurable space one endows it with a σ-algebra.

5. Homological Connectivity, a property related to the homology groups of a topological space.

6. A topological space is said to be locally Contractible if it satisfies the following equivalent conditions:

7. We have Axioms of a topological space, and Axioms for a category and Axioms of groups, semigroups and cohomologies

8. A topological Autorouter uses a different method of mapping the routing space - one that is not geometrically constrained

9. Also directly from the definition, an Aspherical space is a classifying space for its fundamental group (considered to be a topological group when endowed with the discrete topology).

10. A topological group is a mathematical object with both an algebraic structure and a topological structure.

11. Coarser definition, of or relating to a topology on a topological space whose open sets are included among the open sets of a second specified topology on the space

12. In the mathematical field of topology, the Alexandroff extension is a way to extend a noncompact topological space by adjoining a single point in such a way that the resulting space is compact.

13. I think of Compactness as topological finiteness

14. Well, it's actually topological quantum order.

15. Compactness 1 Motivation While metrizability is the analyst’s favourite topological property, Compactness is surely the topologist’s favourite topological property

16. Algebraic structures such as groups to topological spaces

17. Chern classes can be used to construct a homomorphism of rings from the topological K-theory of a space to (the completion of) its rational cohomology.

18. The Situs Autorouter is a Topological Autorouter

19. Topological Glycopolymers as Agglutinator and Inhibitor: Cyclic versus Linear

20. Topological Glycopolymers as Agglutinator and Inhibitor: Cyclic versus Linear

21. A well known topological condition on D-Branes is

22. 312-574 Phone Numbers 2394768684 Albumean Topological mirror symmetry

23. Compactness, in mathematics, property of some topological spaces (a generalization of Euclidean space) that has its main use in the study of functions defined on such spaces

24. Topological groups, together with their homomorphisms, form a category.

25. Covering map, a function from one space to another with uniform local neighborhoods Cover (topology) , a system of (usually, open or closed) sets whose union is a given topological space Branched Covering , generalization of covers which allow for ramification

26. Topological spaces with the Compactness property are called compact spaces.

27. Let(X, T) be a separated topological vector space, B be a closed bounded convex set. T drop property and quasi T drop property of set B is introduced.

28. These topological relationships allow complex spatial modelling and analysis to be performed.

29. That is, the discrete space X is free on the set X in the category of topological spaces and continuous maps or in the category of uniform spaces and uniformly continuous maps.

30. In this video, we look at a topological property called Compactness

31. Topological Glycopolymers as Agglutinator and Inhibitor: Cyclic versus Linear Macromol Rapid Commun

32. this algorithm does a topological sort of an oriented and acyclic graph.

33. As a post-doctoral fellow, he also worked on P-Commutative Topological Algebras.

34. Buck worked on approximation theory, complex analysis, topological algebra, and operations research.

35. In topology and mathematics in general, the Boundary of a subset S of a topological space X is the set of points which can be approached both from S and from the outside of S

36. Piers Bohl, a Latvian mathematician, applied topological methods to the study of differential equations.

37. Many large abelian groups possess a natural topology, which turns them into topological groups.

38. This equivalence provides a precise mathematical formulation of mirror symmetry in topological string theory.

39. Compactness can be thought of a generalization of these properties to more abstract topological spaces

40. In essence, it is a connection between the algebraic and topological sides of operator theory.

41. In physics, these equations express associativity constraints of certain algebras related to topological field theories.

42. In geometry, Chamfering or edge-truncation is a topological operator that modifies one polyhedron into another

43. The topological and analytical indices are both reinterpreted as functions from this ring to the integers.

44. This method, pharmacophore-similarity-based QSAR (PS-QSAR) uses topological pharmacophoric descriptors to develop QSAR models.

45. Its algebraic structure and topology make it into a Lie group, a type of topological group.

46. The stiffness of a griddle body was enhanced using dynamic topological optimization under multiple frequencies constraints.

47. Duality principle is a powerful tool for the analysis of topological structure of power electronic circuits.

48. The Attaching construction is an example of a pushout in the category of topological spaces

49. The invention discloses a multi - autonomous system router level topological treatment system and a method.

50. One of its results, that not every topological algebra is localizable, has become a "well-known counterexample".

51. In one embodiment the 3D renderer creates a physical three dimensional (3D) topological surface from captured images.

52. The category of sheaves of abelian groups on a topological space X is an abelian category, and so it makes sense to ask when a morphism f: B → C of sheaves is injective (a monomorphism) or surjective (an epimorphism).

53. This paper provides some theorems of the alternative for non-linear functions (sublinearconvex) between topological vector spaces.

54. In other words both structures, the algebraic and the topological one, are linked in a natural way.

55. 15 Based on the adjacency matrix network graph, the theoretical proof of the topological arithmetic is given.

56. Her work endeavours to understand the structure of geometric objects by investigation of their algebraic and topological properties.

57. 22 The topological index has good selectivity,(www.Sentencedict.com) and appears solivity for 149 alkanes from ethane to decane.

58. An example of a non-abelian, pre-abelian category is, once again, the category of topological abelian groups.

59. Therefore a mesh has four basic characteristics: geometrical property, topological structure, physical property and time - varying property.

60. This book describes a Bivariant K-theory for bornological algebras, which provides a vast generalization of topological K-theory

61. In every Banach algebra with multiplicative identity, the set of invertible elements forms a topological group under multiplication.

62. The decrease in the Chinese fertility rate has both its substantial space:scale space, structure space, policy space and comparison space, and its conceptual space.

63. The uniform structures allow one to talk about notions such as completeness, uniform continuity and uniform convergence on topological groups.

64. Statuary space may be divided into two parts, physical space and psychological space.

65. They're flying through their space, ocean space.

66. Organize your living space and working space.

67. In terms of the fundamental group in algebraic topology, the HNN extension is the construction required to understand the fundamental group of a topological space X that has been 'glued back' on itself by a mapping f (see e.g. Surface bundle over the circle).

68. Note, however, that the topological dimension of the graph of the Hilbert map (a set in R3) is 1.

69. To use the training space, information space and collaboration space, you must be registered.

70. There are two kinds of storage space: personal storage space and shared storage space.

71. Due to the attainable topological complexity of the design being dependent of the amount of elements, a large amount is preferred.

72. What translates generic public space into qualitative space?

73. Leased space includes office and non-office space, such as archive and warehouse storage space.

74. When file space greatens, new distributive space is not mixed certainly original space is successive.

75. Moving makes space, space will make you sink.

76. Renting of advertising space, including virtual advertising space

77. Before hyperbolic geometry, mathematicians knew about two kinds of space: Euclidean space, and spherical space.

78. His research interests are in topological methods in nonlinear analysis, applications of functional analysis, set-valued analysis, topology, and algebra.

79. The extension property makes β a functor from Top (the category of topological spaces) to CHaus (the category of compact Hausdorff spaces).

80. a Leased space includes office and non-office space, such as archive and warehouse storage space