The set of all compactifications, K(X) of a locally compact, non-compact space X form a complete lattice with βX, the Stone-Čech compactification of X as its largest element, and αX, the one-point compactification of X as its smallest element. For any two locally compact, non-compact spaces X,Y, the lattices K(X), K(Y) are isomorphic
if and only if βX - X and βY - Y are homeomorphic.
βN is the Stone-Čech compactification of the countable infinite discrete space N. There is an isomorphism
between the group of all homeomorphisms of βN and
the group of all permutations of N; so βN has c
homeomorphisms. The space N* =βN - N has 2c homeomorphisms. The
cardinality of the set of orbits of the group of homeomorphisms
of N* onto N* is 2c . If f is a homeomorphism of βN
into itself, then Pk , the set of all k-periodic points
of f is the closure of PkՈN in βN. / Science, Faculty of / Mathematics, Department of / Graduate
| Identifer | oai:union.ndltd.org:UBC/oai:circle.library.ubc.ca:2429/35352 |
| Date | January 1970 |
| Creators | Ng, Ying |
| Publisher | University of British Columbia |
| Source Sets | University of British Columbia |
| Language | English |
| Detected Language | English |
| Type | Text, Thesis/Dissertation |
| Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
Page generated in 0.0021 seconds