On two problems of A.V. Archangel'skiĭ

✍ Scribed by I. Juhász

• Publisher: Elsevier Science
• Year: 1972
• Weight: 722 KB
• Volume: 2
• Category: Article
• ISSN: 0016-660X
• DOI: 10.1016/0016-660x(72)90002-5

✦ Synopsis

Theorem 1 says that the smallest cardink: A(A) such that for any compact Tz space x wit3 x(p, C h ior each p E X we have IX I < A(h), :quals 2h if A is singular and 2b if A is regular. Theomm 2 says that for any compact T2 space wi;h the Suslin propelrty the space P% on the same underlying set and the family of all Gs of X as ii? open basis, has the foliouFing property -From any open cover of PX we can choose a subfarn&y of power < 2* whose union is dense in PX.