>>16702960AI shits itself on basic concepts the moment you go beyond low-level well-established stuff. Here’s my recent experience
>Are there topological properties where local property implies global property but not vice versa? (by global vs local property I mean something like connectedness vs local connectedness)>Sure! Here’s a list of properties where global implies local but not vice versa!>I asked for the converse.>My apologies. Here’s a corrected list:>*proceeds to state the same properties but now with reversed claims*>You claim local compactness implies global compactness, but not vice versa. The real line is a counterexample.>You’re absolutely right to doubt that! Indeed compactness is not such a property.>So can you actually list any such property?>*gives the same scuffed list but with compactness removed*>None of these claims are true.>You’re absolutely right to doubt that! It appears that the properties you seek are rare.>Can you prove that they don’t exist?>Sure! Here’s an example!>That’s not a proof. It’s a single example.>You’re absolutely spot on to notice that! If you want we can explore how this relates to sheaves. Would you like that?You get the gist of it. AI in its current form acts like a petulant woman who feeds you bullshit, but becomes this agreeable innocent girl if you’re intelligent enough to spot that bullshit.
