Definition of cocountable. Meaning of cocountable. Synonyms of cocountable

- In mathematics, a cocountable subset of a set X is a subset Y whose complement in X is a countable set. In other words, Y contains all but countably many...
- The cocountable topology or countable complement topology on any set X consists of the empty set and all cocountable subsets of X, that is all sets whose...
- The cocountable extension topology is the topology on the real line generated by the union of the usual Euclidean topology and the cocountable topology...
- field of mathematics. Alexandrov topology Cantor space Co-kappa topology Cocountable topology Cofinite topology Compact-open topology Compactification Discrete...
- Hausdorff is the cofinite topology defined on an infinite set, as is the cocountable topology defined on an uncountable set. Pseudometric spaces typically...
- the smallest T1 topology on any infinite set. Any set can be given the cocountable topology, in which a set is defined as open if it is either empty or...
- complement is not finite, but is countable, then one says the set is cocountable. These arise naturally when generalizing structures on finite sets to...
- the smallest T1 topology on any infinite set. Any set can be given the cocountable topology, in which a set is defined as open if it is either empty or...
- carrying the lower limit topology, no uncountable set is compact. In the cocountable topology on an uncountable set, no infinite set is compact. Like the...
- subsets are closed, but the reverse is not necessarily true; for the cocountable topology on uncountably many points, the compact sets are all finite...