equivalently if arbitrary unions of closed sets are closed. These are precisely the finitely generated members of the category of topological spaces and continuous maps. Zero-dimensional. A space is zero-dimensional if it has a base of clopen sets. These are precisely the spaces with a small inductive dimension of 0. Almost discrete. A space is almost discrete if every open set is closed (hence clopen). The almost discrete spaces are precisely the finitely generated zero-dimensional spaces. Boolean. A space is Boolean if it is zero-dimensional, compact and Hausdorff (equivalently, totally disconnected, compact and Hausdorff). These are precisely the spaces that are homeomorphic to the Stone spaces of Boolean algebras. Reidemeister torsion -resolvable. A space is said to be κ-resolvable (respectively: almost κ-resolvable) if it contains κ dense sets that are pairwise disjoint (respectively: almost disjoint over the ideal of nowhere dense subsets). If the space is not -resolvable then it is called -irresolvable. Maximally resolvable. Space is maximally resolvable if it is -resolvable, where Number is called dispersion character of Strongly discrete. Set is strongly discrete subset of the space if the points in may be separated by pairwise disjoint neighborhoods. Space is said to be strongly discrete if every non-isolated point of is the accumulation point of some strongly discrete set. Non-topological properties There are many examples of properties of metric spaces, etc, which are not topological properties. To show a property is not topological, it is sufficient to find two homeomorphic topological spaces such that has , but does not have . For example, the metric space properties of boundedness and completeness are not topological properties. Let and be metric spaces with the standard metric. Then, via the homeomorphism . However, is complete but not bounded, while is bounded but not complete. See also Homology and cohomology Homotopy group and Cohomotopy group Citations References [2] Simon Moulieras, Maciej Lewenstein and Graciana Puentes, Entanglement engineering and topological protection by discrete-time quantum walks, Journal of Physics B: Atomic, Molecular and Optical Physics 46 (10), 104005 (2013). https://iopscience.iop.org/article/10.1088/0953-4075/46/10/104005/pdf Homeomorphisms ru:Топологический инвариант