Show that U(x0, ε) is an open set. I'm reading Analysis on Manifolds by Munkres. This question is in the review on Topology section. And I've just recently been introduced to basic-basic topology from Principles of Mathematical Analysis by Rudin. I'm not really certain where to begin on this, nor can I find a sufficient definition of open set to somewhat utilize. Any help on where to begin would be appreciated. This doesn't seem like it would be difficult or long, just kind of in unfamiliar ground here. Thanks in advanced.