On uniform connectedness
Dharmanand Baboolal · International Journal of Mathematics and Mathematical Sciences · 1988
The concept of uniform connectedness, which generalizes the concept of well-chainedness for metric spaces, is used to prove the following: (a) If two points a and b of a compact Hausdorff uniform space (X,U) can be Joined by a U-chain for every U E [, then they lie together in the same component of X; (b) Let (X,U) be a compact Hausdorff uniform space, A and B non-empty disjoint closed subsets of X such that no component of X intersects both A and B. Then there exists a separation X XAU XB, where X A and X B are disjoint compact sets containing A and B respectively.These generalize the corresponding results for metric spaces.