topological structure in a sentence

Examples

1. C-K theory was shown by Hatchuel and Weil which are both based on topological structures for design modeling.
2. The variability of sources and destinations in this model has a drastic effect on the topological structure underlying the solution.
3. These sets can be given a natural topological structure : the Zariski Riemann space of " K / k ".
4. To define a closeness relation between two sets the topological structure is too weak and we have to use a uniform structure.
5. Examples are homomorphisms, which preserve algebraic structures; homeomorphisms, which preserve topological structures; and diffeomorphisms, which preserve differential structures.
6. This topology can be derived from the Vietoris topology construction, a topological structure on all non-empty subsets of a space.
7. The final equivalent condition shows that the class of sequential spaces consists precisely of those spaces whose topological structure is determined by convergent sequences in the space.
8. In the generalized transportation problem the topological structure of the evolving iterative solution is a set of disconnected loops each with attached branched sidechains ( trees ).
9. The conceptual difference between uniform and topological structures is that, in a uniform space, one can formalize certain notions of relative closeness and closeness of points.
10. Infinite products are also defined by the topological structure; it can be seen that an infinite product converges if and only if the sequence of its factors converges to 1.