Definition of Collectionwise. Meaning of Collectionwise. Synonyms of Collectionwise

- In mathematics, a topological space X {\displaystyle X} is called collectionwise normal if for every discrete family Fi (i ∈ I) of closed subsets of X...
- of topology, a topological space X {\displaystyle X} is said to be collectionwise Hausdorff if given any closed discrete subset of X {\displaystyle X}...
- the space of functions from R to itself is Tychonoff but not normal. Collectionwise normal space – Property of topological spaces stronger than normality...
- complete Boolean algebras. An extremally disconnected first-countable collectionwise Hausdorff space must be discrete. In particular, for metric spaces,...
- first-countable space is regular. Every normal countably compact space is collectionwise normal. The product of a compact space and a countably compact space...
- other metrization theorems, e.g. the Moore metrization theorem – a collectionwise normal, Moore space is metrizable – is a direct consequence. Unlike...
- Hausdorff (or T5). Every monotonically normal space is hereditarily collectionwise normal. The image of a monotonically normal space under a continuous...
- general topology, earning a master's degree in 1957 with the thesis Collectionwise normal and strongly paracompact spaces on strengthened definitions for...
- be strengthened in this way. Moore himself proved the theorem that a collectionwise normal Moore space is metrizable, so strengthening normality is another...
- the set of all real numbers endowed with the cofinite topology shows. Collectionwise normal space – Property of topological spaces stronger than normality...