Timeline for A souped-up version of a question asked previously about uncountable subsets of topological spaces
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 18, 2014 at 22:39 | comment | added | Garabed Gulbenkian | Thanks. That certainly proves that property P does not imply second countability and one can take any second countable topological space for X. | |
| Mar 17, 2014 at 20:35 | comment | added | Santi Spadaro | The disjoint sum of spaces $(X, \sigma)$ and $(Y, \tau)$ (where $X \cap Y=\emptyset$) is defined as the topology on $X \cup Y$ where a set $U$ is open if and only if $U \cap X \in \sigma$ and $U \cap Y \in \tau$. | |
| Mar 17, 2014 at 20:05 | comment | added | Garabed Gulbenkian | I must apologize! My previous comment is topsy-turvy. X should be the space that has property P and Z should be the countable space that is not second countable. But I would still like to know what is meant by the "topological sum" of these two spaces. | |
| Mar 17, 2014 at 19:42 | comment | added | Garabed Gulbenkian | @ Santi Sparado: Thanks for your answer. Perhaps you could clarify one point. Let Z be the space having property P. Is Y the set union of X and Z and is the set union of any base of X with any base of Z, a base of Y? I am just trying to understand clearly what "topological sum" means | |
| Mar 16, 2014 at 23:51 | history | edited | Santi Spadaro | CC BY-SA 3.0 |
added 6 characters in body
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| Mar 16, 2014 at 23:40 | history | answered | Santi Spadaro | CC BY-SA 3.0 |