As anyone who fought their way through analysis in their first term will know: very little in maths comes easy. The most fundamental and fundamentally obvious properties of spaces can be hidden in a world of axiomatic obfuscation, leaving you wondering whether such an obvious truth should be a fair assumption to make. More often than not the answer is "No!" "...and go sit in the corner 'til you learn to be a proper mathematician!"- these dubious assumptions need to be proved from first principles, and it is not likely to be easy.