Results related to the Michael line

✍ Scribed by Kiiti Morita

• Book ID: 104295234
• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 240 KB
• Volume: 82
• Category: Article
• ISSN: 0166-8641
• DOI: 10.1016/s0166-8641(97)00049-7

✦ Synopsis

For a Hausdorff space (X, 7) with a topology r and Y C X, let (X,7(X, Y)) be the space X with the topology 7(X, Y) defined by {G U B 1 G E T, B c Y}. We prove that in case (X, 7) is paracompact and perfectly normal with Y metrizable, (X,7(X; Y)) x (Y, T/Y) is normal iff Y is F, in (X, T). An example is also given showing that without perfect normality of (X, 7) this result is not true even if (X, T) is hereditarily paracompact.