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

2. I think of Compactness as topological finiteness

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

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

5. Algebraic structures such as groups to topological spaces

6. The Situs Autorouter is a Topological Autorouter

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

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

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

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

11. 312-574 Phone Numbers 2394768684 Albumean Topological mirror symmetry

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

42. 15 Based on the adjacency matrix network graph, the theoretical proof of the topological arithmetic is given.

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

44. 22 The topological index has good selectivity,(www.Sentencedict.com) and appears solivity for 149 alkanes from ethane to decane.

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

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

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

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

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

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

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

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

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

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

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

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

57. The graph of a continuous function of two variables, defined over a connected open subset of R2 is a topological surface.

58. The fundamental principle and Graph Analysis Method (GAM)for determining logical names of topological equivalent multistage interconnection network(MIN)are proposed.

59. To get back to actual topological spaces, there is a geometric realization functor which turns simplicial sets into compactly generated Hausdorff spaces.

60. Group representations are an organizing principle in the theory of finite groups, Lie groups, algebraic groups and topological groups, especially (locally) compact groups.

61. EU-funded researchers have introduced topological notions to non-mainstream many-valued logic and related algebras with interesting implications for other areas of mathematics.

62. Requirement is, that the cyclic order of the adjacent vertices for every vertex of the graph is found out by a topological algorithm for planarity.

63. In abstract algebra, a completion is any of several related functors on rings and modules that result in complete topological rings and modules.

64. Synthetic non-Abelian gauge fields have emerged as a new way for studying the topological phases of matter, providing new insights in optics and photonics

65. On the basis of the principle, the OET (orbital-energy topological index) was proposed by revising the valence electron distance matrix with the orbital energy.

66. 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.

67. Based on the formation of origami triangles, combined with the use of the latest parametric design tools and topological analysis, the unique structural design was formed.

68. Rather than using workspace coordinate information as a frame of reference (dividing it into a grid), a topological Autorouter builds a map using only the relative positions

69. 14 This paper discusses the application of adjacency matrix at the algorithm's analysis for traversing Graph, Minimum cost Spanning Tree, Topological sort and Critical Path.

70. 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).

71. Taking structure weight as objective function, the optimization model of overweight breech of a type of automatic weapon was established, and its structure topological optimization was performed.

72. For example, in the category of topological abelian groups, the image of a morphism actually corresponds to the inclusion of the closure of the range of the function.

73. 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

74. Topics include algebraic combinatorics, combinatorial geometry, combinatorial number theory, combinatorial optimization, designs and configurations, enumerative combinatorics, extremal combinatorics, graph theory, ordered sets, random methods, and topological combinatorics.

75. In the A-model of topological string theory, physically interesting quantities are expressed in terms of infinitely many numbers called Gromov–Witten invariants, which are extremely difficult to compute.

76. 1955 Alexander Grothendieck in lectures in Kansas defines abelian category and presheaf, and by using injective resolutions allows direct use of sheaf cohomology on all topological spaces, as derived functors.

77. Other common examples: The category of (left) modules over a ring R, in particular: the category of vector spaces over a field K. The category of (Hausdorff) abelian topological groups.

78. 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

79. 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.

80. Applying a D-triangulation on the facial feature points, a precise and topological isomorphic mapping is established between 3D mesh and texture. The texture mapping with high quality can be obtained.