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EnglishIn this note a T1 formal space (T1 set generated locale) is a formal space whose points are closed as subspaces. Any regular formal space is T1. We introduce the more general notion of T1* formal space, and prove that the class of points of a weakly set-presentable T1* formal space is a set in the constructive set theory CZF. The same also holds in constructive type theory. We then formulate separation properties Ti* for (class-sized) constructive topological spaces (ct-spaces), strengthening separation properties discussed elsewhere. Finally we relate the Ti* properties for ct-spaces with corresponding properties of formal spaces.
| Titolo: | On the T1 axiom and other separation properties in constructive topology. |
| Autori: | |
| Data di pubblicazione: | 2009 |
| Rivista: | |
| Abstract: | In this note a T1 formal space (T1 set generated locale) is a formal space whose points are closed as subspaces. Any regular formal space is T1. We introduce the more general notion of T1* formal space, and prove that the class of points of a weakly set-presentable T1* formal space is a set in the constructive set theory CZF. The same also holds in constructive type theory. We then formulate separation properties Ti* for (class-sized) constructive topological spaces (ct-spaces), strengthening separation properties discussed elsewhere. Finally we relate the Ti* properties for ct-spaces with corresponding properties of formal spaces. |
| Handle: | http://hdl.handle.net/11562/324112 |
| Appare nelle tipologie: | 01.01 Articolo in Rivista |
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