I want to know the example which satisfies the following.
X is topological space.
for every point x,y in X, there exist open nbhd Ux,Uy of x,y which are homeomorphic.
X has some kind of good conditions, i.e hausdorff,locally connected,locally compact, 2nd countable.. etc..
X is not locally Euclidean .
I think.... the thing like topologically homogeneous space which is not manifold. but I can't find the good example.
additional supplement
In fact, another goal of my question is this. "How can I make locally euclidean property from the other topological properties."
