Properties and Counterexamples on Generalizations of Lindelof Spaces
In this thesis, generalizations of Lindelof spaces that depend on open covers and regularly open covers are studied. Namely: nearly Lindelof, almost Lindelof and weakly Lindelof spaces. And generalizations of regular-Lindelof spaces that depend on regular covers are also studied. Namely: nearly r...
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis |
| Language: | English English |
| Published: |
2002
|
| Subjects: | |
| Online Access: | http://psasir.upm.edu.my/id/eprint/9366/1/FSAS_2002_10_A.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | In this thesis, generalizations of Lindelof spaces that depend on open covers
and regularly open covers are studied. Namely: nearly Lindelof, almost
Lindelof and weakly Lindelof spaces. And generalizations of regular-Lindelof
spaces that depend on regular covers are also studied. Namely: nearly regularLindelof,
almost regular-Lindelof and weakly regular-Lindelof spaces. Some
properties and characterizations of these six generalizations of Lindeiof spaces
are given. The relations among them are studied and some counterexamples
are given in order to prove that the studied generatizations are proper generalizations
of Lindelof spaces. Subspaces and subsets of these spaces are studied.
We show that some subsets of these spaces inherit these covering properties
and some others they do not
Moreover, semiregular property on these spacess is studied to establish that
all of these properties are semiregutar properties on the contrary of Lindelof property which is not a semiregular property. Mappings and generalized cont
inuous functions are also studied on these generalizations and we prove that
these properties are topological properties. Relations and some properties of
many decompositions of continuity and generalized continuity that recently
defined and studied are given. Counterexamples are also given to establish the
relations among these generalizations of continuity. We show that some proper
mappings preserve these topological properties such as: 6-continuity preserves
nearly Lindelof property. O-continuity preserves almost Lindelof property. Rmaps
preserve nearly regular-Lindelof property. Almost continuity preserves
weakly Lindelof, almost regular-Lindelof and weakly regular-Lindelof properties.
Moreover, we give some conditions on the functions or on the spaces to
prove that weak forms of continuity preserve some of these covering properties
under these conditions.
The product property on these generalizations is also studied. We show
that these topological properties, as in the case of most non-compact properties,
are not preserved by product, even under a finite product. Some conditions
are given on these generalizations to prove that these properties are
preserved by finite product under these conditions. We show that, in weak
P-spaces, finite product of nearly Lindelof spaces is nearly Lindelof and finite
product of weakly Lindelof spaces is almost Lindelof. |
|---|