이산 공간

노트

위키데이터

• ID : Q175116

말뭉치

1. In discrete space, one agent occupies one cell.
2. The columns and rows define cells of the discrete space.
3. In this sense, the theory of discrete spaces is equivalent to the theory of partially ordered sets.
4. Given any set, there is a unique topology on it making it into discrete space.
5. Any subspace of a discrete space is discrete under the induced topology.
6. The underlying uniformity on a discrete metric space is the discrete uniformity, and the underlying topology on a discrete uniform space is the discrete topology.
7. For example, any group can be considered as a topological group by giving it the discrete topology, implying that theorems about topological groups apply to all groups.
8. While discrete spaces are not very exciting from a topological viewpoint, one can easily construct interesting spaces from them.
9. A product of countably infinitely many copies of the discrete space {0,1} is homeomorphic to the Cantor set; and in fact homeomorphic to the Cantor set if we use the product uniformity on the product.
10. The discrete topology is the finest topology that can be given on a set, i.e., it defines all subsets as open sets.
11. Since the intersection of two open sets is open, and singletons are open, it follows that X is a discrete space.
12. A product of countably infinite copies of the discrete space of natural numbers is homeomorphic to the space of irrational numbers, with the homeomorphism given by the continued fraction expansion.
13. We define the dimension on a discrete space by means of axioms based on an obvious geometrical background.
14. It explains how to construct new discrete spaces and describes in this connection several three-dimensional closed surfaces with some topological singularities.
15. In this paper we propose a discrete space (i.e., grid-based) model for dispersal processes in continuous space.
16. A discrete space is, in general, an object of a concrete category Sp Sp of spaces that is free on its own underlying set.
17. But there were problems with relativistic invariance, and after ideas of renormalization developed in the 1940s, discrete space seemed unnecessary, and has been out of favor ever since.

메타데이터

위키데이터

• ID : Q175116

Spacy 패턴 목록

• [{'LOWER': 'discrete'}, {'LEMMA': 'space'}]