QUOTIENTS OF PROXIMITY SPACES 589
... and (P5) is satisfied. Note that ô' is easily separated and ô'<ô. It follows from our assumption that i:(X, Ô)-*(X, ô') is a one-to-one /»-quotient map, and so, by Theorem 2.2, ô=ô'. This contradicts the definition of ô'; therefore, (X, ô) is compact. Conversely, assume (X, ô) is compact and let /be ...
... and (P5) is satisfied. Note that ô' is easily separated and ô'<ô. It follows from our assumption that i:(X, Ô)-*(X, ô') is a one-to-one /»-quotient map, and so, by Theorem 2.2, ô=ô'. This contradicts the definition of ô'; therefore, (X, ô) is compact. Conversely, assume (X, ô) is compact and let /be ...
![arXiv:math/0302340v2 [math.AG] 7 Sep 2003](http://s1.studyres.com/store/data/014807023_1-69877329430c783f1dba3c51b4839685-300x300.png)
43. Nearness in review Author: Zohreh Vaziry and Sayyed Jalil
... EF-proximity spaces and δ-maps and Cont of all contiguity spaces and contiguity maps as nicely embedded (either bireflective or bicoreflective) full subcategories. In this paper we have some new results on objects of the category T-Near of all topological near spaces and nearness preserving maps whi ...
... EF-proximity spaces and δ-maps and Cont of all contiguity spaces and contiguity maps as nicely embedded (either bireflective or bicoreflective) full subcategories. In this paper we have some new results on objects of the category T-Near of all topological near spaces and nearness preserving maps whi ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.