I'm really just having trouble figuring out what a question is asking. Here's the question: My problem is really just that in proving that say regularity is a local property, I'm not sure what to use as a subspace. I could take a given base set and then consider the rest of the base sets intsersected with it as sub-base sets for that original base set. I'm not sure if that's what I'm supposed do though. Does that sound like the right approach? Any help would be swell.