If X is a topological space and Y is a ring of closed sets, then a necessary and sufficient condition for the Wallman space W(X,F) to be a compactification of X is that X be T1 andYF separating. A necessary and sufficient condition for a Wallman compactification to be Hausdoff is that F be a normal base. As a result, not all T, compactifications can be of Wallman type. One point and finite Hausdorff compactifications are of Wallman type.
| Identifer | oai:union.ndltd.org:unt.edu/info:ark/67531/metadc504392 |
| Date | 12 1900 |
| Creators | Liu, Wei-kong |
| Contributors | Mohat, John T., 1924-, Allen, John Ed, 1937- |
| Publisher | North Texas State University |
| Source Sets | University of North Texas |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
| Format | iii, 30 leaves, Text |
| Rights | Public, Liu, Wei-kong, Copyright, Copyright is held by the author, unless otherwise noted. All rights reserved. |
Page generated in 0.1822 seconds