Timeline for Existence of space $Z$ such that $\text{Cont}(X,Z) \cong X$
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 8 at 20:02 | comment | added | daniel gratzer | I think the question has its quantifiers change, but after the edit the answer should be yes. Using domain theory, one can produce a continuous domain $D$ such that $D \cong (D \to D)$ and the category of continuous domains embeds as a full subcategory into the category of topological spaces | |
| May 8 at 18:21 | history | edited | Dominic van der Zypen | CC BY-SA 4.0 |
added 36 characters in body
|
| May 8 at 13:11 | comment | added | Thomas Rot | I dont think so. What if X is the two point space with the discrete topology. Then for any Z the continous maps are in bijection with ordinary maps. Cont(X,Z) has either one element (if Z has one element), or a cardinality strictly larger than 2 if Z has more than one element. | |
| May 8 at 13:04 | history | asked | Dominic van der Zypen | CC BY-SA 4.0 |