α-sober spaces via the orthogonal closure operator
Each ordinal alpha equipped with the upper topology is a T0-space. It is well known that for alpha=2 the reflective hull of alpha in Top0 is the subcategory of sober spaces. Here, we define alpha-sober space for every ordinal alpha in such a way that the reflective hull of alpha in Top0 is the subca...
| Autor principal: | |
|---|---|
| Formato: | article |
| Idioma: | eng |
| Publicado em: |
2015
|
| Assuntos: | |
| Texto completo: | http://hdl.handle.net/10400.19/2852 |
| País: | Portugal |
| Oai: | oai:repositorio.ipv.pt:10400.19/2852 |
| Resumo: | Each ordinal alpha equipped with the upper topology is a T0-space. It is well known that for alpha=2 the reflective hull of alpha in Top0 is the subcategory of sober spaces. Here, we define alpha-sober space for every ordinal alpha in such a way that the reflective hull of alpha in Top0 is the subcategory of alpha-sober spaces. Moreover, we obtain an order-preserving bijective correspondence between a proper class of ordinals and the corresponding (epi)reflective hulls. Our main tool is the concept of orthogonal closure operator, introduced by the authour in a previous paper. |
|---|