a note on strongly lindel¨of spaces
... sets is open. In [6] it is shown that each L–closed Lindelöf space is a P –space and that a Hausdorff Lindelöf space is L–closed if and only if it a P –space. Using this result and Theorem 3.1 we immediately obtain Theorem 3.2 Let (X, τ ) be Hausdorff and strongly Lindelöf. Then (X, τ ) is maxima ...
... sets is open. In [6] it is shown that each L–closed Lindelöf space is a P –space and that a Hausdorff Lindelöf space is L–closed if and only if it a P –space. Using this result and Theorem 3.1 we immediately obtain Theorem 3.2 Let (X, τ ) be Hausdorff and strongly Lindelöf. Then (X, τ ) is maxima ...
F-SINGULARITIES AND FROBENIUS SPLITTING
... Canonical divisors are divisor classes on varieties over fields. This is much more ambiguous on general schemes since ωX can be twisted by any line bundle and still be a canonical module (we only defined it locally). Theorem 2.4. [Har66] Let R ⊆ S be a finite inclusion of rings with dualizing comple ...
... Canonical divisors are divisor classes on varieties over fields. This is much more ambiguous on general schemes since ωX can be twisted by any line bundle and still be a canonical module (we only defined it locally). Theorem 2.4. [Har66] Let R ⊆ S be a finite inclusion of rings with dualizing comple ...
Chapter IV. Topological Constructions
... of partition T containing f (A). This map is denoted by f /S, T and called the quotient map or factor map of f (with respect to S and T ). 20.O. Formulate and prove for f /S, T a statement generalizing 20.N. A map f : X → Y determines a partition of the set X into nonempty preimages of the elements ...
... of partition T containing f (A). This map is denoted by f /S, T and called the quotient map or factor map of f (with respect to S and T ). 20.O. Formulate and prove for f /S, T a statement generalizing 20.N. A map f : X → Y determines a partition of the set X into nonempty preimages of the elements ...
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.