# Open Cover

### Some articles on open cover, open, cover, covers:

Paracompact Space - Paracompact Hausdorff Spaces - Partitions of Unity - Proof That Paracompact Hausdorff Spaces Admit Partitions of Unity
... space is paracompact if and only if it every open cover admits a subordinate partition of unity ... Lemma 1 If is a locally finite open cover, then there exists open sets for each, such that each and is a locally finite refinement ... Lemma 2 If is a locally finite open cover, then there are continuous functions such that and such that is a continuous function which is always non-zero and finite ...
Compact Space - Theorems
... X has a sub-base such that every cover of the space by members of the sub-base has a finite subcover (Alexander's sub-base theorem) Every net on X has a convergent subnet (see ... Every open cover of A has a finite subcover ... as the collection of all singleton points of the space is an open cover which admits no finite subcover ...
Leray Cover
... In mathematics, a Leray cover(ing) is a cover which allows for easy calculation of cohomology ... On the other hand, Čech cohomology with respect to an open cover is well-suited to calculation, but of limited usefulness because it depends on the open cover chosen, not only on the sheaves and the space ... By taking a direct limit of Čech cohomology over arbitrarily fine covers, we obtain a Čech cohomology theory that does not depend on the open cover chosen ...
Shrinking Space
... is said to be a shrinking space if every open cover admits a shrinking ... A shrinking of an open cover is another open cover indexed by the same indexing set, with the property that the closure of each open set in the shrinking lies inside the ... In a normal space, every locally finite, and in fact, every point finite open cover admits a shrinking ...
Finite Morphism - Morphisms of Finite Type
... The technical definition is as follows let be an open cover of by affine schemes, and for each let be an open cover of by affine schemes ... If in addition the open cover can be chosen to be finite, then f is called of finite type ...

### Famous quotes containing the words cover and/or open:

Every individual ought to know at least one poet from cover to cover: if not as a guide through the world, then as a yardstick for the language.
Joseph Brodsky (b. 1940)

Some collaboration has to take place in the mind between the woman and the man before the art of creation can be accomplished. Some marriage of opposites has to be consummated. The whole of the mind must lie wide open if we are to get the sense that the writer is communicating his experience with perfect fullness.
Virginia Woolf (1882–1941)