A question on the proof of 14 distinct sets can be formed by complementation and closure In Munkres, problem 20 of Section 2-6, it says that 14 distinct sets can be formed by complementation and closure. I see only five so far.
Let f be the function of closure mapping and g be the function of complementation mapping.
It is clear, f,g, fg,gf, and gfg are the 5 of 15 distinct sets. What are the rests? Was there any topological argument associated with it? How can I understand this intuitively and pictorially?

The following page lists the rest, and since it lets you experiment in real time, may also accelerate your intuitive and pictorial understanding:
http://www.maa.org/sites/default/files/images/upload_library/60/bowron/k14.html
Though the 14-set theorem is more algebraic than topological, constructing a Kuratowski 14-set in the reals will enrich your understanding of topology.
