I second Hatcher. His AT book is a goto for me. He also has introduction to point set topology notes on his site which are appropriate for someone without a math background.
Recently I've been reading 'Introduction to Topology' by Mendelson, it's very good so far, although I'm skipping the exercises for the first reading (First reading to try and get the concepts, second reading to solidify them).
It's actually availible free from archive.org[0], which is a huge plus.