Baire spaces, k-spaces, and some properly hereditary properties
A topological property is properly hereditary property if whenever every proper subspace has the property, the whole space has the property. In this note, we will study some topological properties that are preserved by proper subspaces; in fact, we will study the following topological properties: Ba...
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.3697 |
| Summary: | A topological property is properly hereditary property if
whenever every proper subspace has the property, the whole space
has the property. In this note, we will study some topological
properties that are preserved by proper subspaces; in fact, we
will study the following topological properties: Baire spaces,
second category, sequentially compact, hemicompact, δ-normal, and spaces having dispersion points. Also, we
will solve some open problems raised by Al-Bsoul (2003) and Arenas
(1996) and conclude this note by some open problems. |
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| ISSN: | 0161-1712 1687-0425 |