Sentence examples for open sets from inspiring English sources

Define the open sets (3.3).

Clearly, the two open sets are disjoint.

The union of any family of open sets is open.

Clearly, F Φ and F A are soft open sets.

Assume that and are two bounded open sets in with,.

We also need to define axially symmetric open sets.

Császár [2] introduced generalized open sets in 1997.

Given arbitrary nonempty open sets, we fix and pairs of nonempty open sets in the corresponding spaces,, such that (2.10).

So while there are uncountably many open sets, there are only countably many effective open sets; the later notion is much more restrictive.

A new characterization of the Daugavet property in terms of weak open sets is given.

A set of reals is nowhere dense iff its closure under limits contains no open sets.