Nearly metacompact spaces

✍ Scribed by Elise Grabner; Gary Grabner; Jerry E. Vaughan

• Book ID: 104295515
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 112 KB
• Volume: 98
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(98)00107-2

✦ Synopsis

A space X is called nearly metacompact (meta-Lindelöf) provided that if U is an open cover of X then there is a dense set D ⊆ X and an open refinement V of U that is point-finite (point-countable) on D. We show that countably compact, nearly meta-Lindelöf T 3 -spaces are compact. That nearly metacompact radial spaces are meta-Lindelöf. Every space can be embedded as a closed subspace of a nearly metacompact space. We give an example of a countably compact, nearly meta-Lindelöf T 2 -space that is not compact and a nearly metacompact T 2 -space which is not irreducible.