The Dink Network

The maths here looks sorta like the one I've had in the beginning of this year or in the previous course about logic and set theory. In theory, I should be able to solve 1 and 2.. for the two others I don't know the mathematical definition of "continuous" so I don't really know how to start there - I know what it means but it's usually easier to take the mathematical definition and work from there (like "for all a in set A ,there is a b in set B etc") And I'm not that good at proving things in mathematics anyway