Yeap. There is some stuff about this in the wiki article actually. Here it is again:
http://en.wikipedia.org/wiki/Neighbourhood_%28mathematics%29#Topology_from_neighbourhoods
hmmmm
well what i wrote down is the definition of neighbourhood given in the book I am trying to read. and it is also the definition given on this page
http://en.wikipedia.org/wiki/Neighbourhood_%28mathematics%29
munkres topology book has the following definition/remarks:
thank you for your...
Sorry this is a new subject to me so please bear with me.
I'm having difficulty with two things
First, we are talking about neighborhoods of arbitrary topological spaces. 'Invariance of domain' is a theorem about R^n. How does this theorem, which is restricted to R^n say anything about sets...
hey guys
im trying to prove a fact. it is supposed to be really easy but I am having some trouble. this is it:
http://en.wikipedia.org/wiki/Topological_manifold
"It follows from invariance of domain that Euclidean neighborhoods are always open sets."
Invariance of Domain -...