I am starting to study some lecture notes about metric geometry and I would appreciate it if someone could some questions regarding the notion of the tangent cone.
Consider 3 half lines joined by their point of origin. You get a network of 3 roads and a junction point. This is an Aleksandrov space of non-positive curvature. It is even geodesically complete. Now, I am having trouble defining the tangent cone at this junction point:
- Is it isometric or BiLipschitz to $R^k$ for some $k>0$ ?
- What is the Hausdorff dimension of the space at this point ? is it 1 ?
- is the junction point the boundary of the Aleksandrov space ?
These questions might be trivial so I apologize in advance but I just didn't find enough examples that talk about this.