1. A note on star Lindelöf, first countable and normal spaces
- Creator:
- Xuan, Wei-Feng
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- star Lindelöf space, first countable space, normal space, and countable extent
- Language:
- English
- Description:
- A topological space X is said to be star Lindelöf if for any open cover U of X there is a Lindelöf subspace A ⊂ X such that St(A, U) = X. The “extent” e(X) of X is the supremum of the cardinalities of closed discrete subsets of X. We prove that under V = L every star Lindelöf, first countable and normal space must have countable extent. We also obtain an example under MA + ¬CH, which shows that a star Lindelöf, first countable and normal space may not have countable extent.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public