Hey guys, so this question was posted a while ago by someone so I don't know if this is reposting, but my question about it is different.
Suppose f: K->(- , ), K is compact, and f has a finite limit at each point of K, but may not be continuous on K. Show that f is bounded in two ways: (i) by using the definititon of compactness in terms of open covers, and (ii) by using the sequential characterization of compactness. Is the same conclusion valif if we drop the assumption that the limit of f is finite?
For some reason I can't find these specific definitions in the book I'm using, but I've come acrossed problems that deal with them, similar to this one. I kinda want to battle out the problems I've been working on on my own but I feel like seeing the proof for this problem for part one and part two would give me a better understanding of what's going on here and and lead me to figure out my stuff. Thanks!