I stumbled across this "dictionary for noncommutative topology" <http://planetmath.org/noncommutativetopology>
and I would be very interested in learning more on the subject, particularly I'd like to see why these results are true. 


What is the reference to the results in section 3 of the above linked page?



Specific Reference? Noncommutative topology and C^* algebras
*Les C$^\*$-algèbres et leurs représentations* (answers most of these). 


Find it [here](http://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=6&ved=0CDgQFjAF&url=http%3A%2F%2Fiecl.univ-lorraine.fr%2F~Nicolas.Prudhon%2Fgnc%2Fbibliographie%2FOperator%2520Algebras%2FDixmier%2520%5B1977a%2C%2520288pp%5Dh---C-star-algebras.pdf&ei=_vHHU8jvAtCgyAS7qoAw&usg=AFQjCNEw7EMCQDbfHD9TKhg8VAvQF1qTLw&bvm=bv.71198958,d.aWw&cad=rja). That "dictionary" can also be found [here](http://www.google.ca/url?sa=t&rct=j&q=&esrc=s&source=web&cd=7&ved=0CFQQFjAG&url=http%3A%2F%2Fmath.aalto.fi%2Fopetus%2Fharmanal%2Fpruju%2Fcalg04.pdf&ei=CPXHU4W7N5K3yASQrYCgBg&usg=AFQjCNEwD0IBkTU17mU6IcFfV5BNqLdENg&sig2=r4ukgeWZhIAVIXaRlgsD6A&bvm=bv.71198958,d.aWw&cad=rja).


