Characterizations of Strongly Compact Spaces
A topological space (X,τ) is said to be strongly compact if every preopen cover of (X,τ) admits a finite subcover. In this paper, we introduce a new class of sets called -preopen sets which is weaker than both open sets and -open sets. Where a subset A is said to be -preopen if for each x∈A there...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
|
| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2009/573038 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | A topological space (X,τ) is said to be strongly compact if every preopen cover of (X,τ) admits a finite subcover. In this paper, we introduce a new class of sets called -preopen sets which is weaker than both open sets and -open sets. Where a subset A
is said to be -preopen if for each x∈A
there exists a preopen set Ux
containing x such that Ux−A is a finite
set. We investigate some properties of the sets. Moreover, we obtain new characterizations and preserving theorems of strongly compact spaces. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |