Derived algebraic geometry
... functors are defined. Even if our ultimate interest is only in reduced schemes (such as smooth algebraic varieties), it is useful to consider these schemes as defining functors on possibly non-reduced rings. For example, the non-reduced scheme X = Spec C[]/(2 ) is an interesting test object which ...
... functors are defined. Even if our ultimate interest is only in reduced schemes (such as smooth algebraic varieties), it is useful to consider these schemes as defining functors on possibly non-reduced rings. For example, the non-reduced scheme X = Spec C[]/(2 ) is an interesting test object which ...
barmakthesis.pdf
... That means that for any two points of X0 there exists an open set which contains only one of them. Therefore, when studying homotopy types of finite spaces, we can restrict our attention to T0 -spaces. In [37], Stong defines the notion of linear and colinear points, which we call up beat and down be ...
... That means that for any two points of X0 there exists an open set which contains only one of them. Therefore, when studying homotopy types of finite spaces, we can restrict our attention to T0 -spaces. In [37], Stong defines the notion of linear and colinear points, which we call up beat and down be ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.