Generalized Minimal Closed Sets in Topological Spaces.
... open set in X then Y I U is a minimal open set in Y. Proof: Let U be any minimal open set in X such that Y I U is not a minimal open set in Y. Then there exists an open set G≠ Y in Y such that G ⊆ Y I U where G = Y I H and H is an open set in X. Then Y I H ⊆ Y I U, which implies that H ⊆ U, This is ...
... open set in X then Y I U is a minimal open set in Y. Proof: Let U be any minimal open set in X such that Y I U is not a minimal open set in Y. Then there exists an open set G≠ Y in Y such that G ⊆ Y I U where G = Y I H and H is an open set in X. Then Y I H ⊆ Y I U, which implies that H ⊆ U, This is ...
arXiv:1311.6308v2 [math.AG] 27 May 2016
... 2.1.1. The category of models. A model X is a triple (X , X, ψX ) such that X and X are quasi-compact and quasi-separated (qcqs) algebraic spaces, and ψX : X → X is a separated schematically dominant morphism. The spaces X and X are called the model space and the generic space of X respectively. We ...
... 2.1.1. The category of models. A model X is a triple (X , X, ψX ) such that X and X are quasi-compact and quasi-separated (qcqs) algebraic spaces, and ψX : X → X is a separated schematically dominant morphism. The spaces X and X are called the model space and the generic space of X respectively. We ...
A survey of ultraproduct constructions in general topology
... made good use of this idea, introducing a notion of finiteness in a category by means of the simple bridging result that says a relational structure is finite if and only if all diagonal maps from that structure into its ultrapowers are isomorphisms. An object A in a category C equipped with ultrapr ...
... made good use of this idea, introducing a notion of finiteness in a category by means of the simple bridging result that says a relational structure is finite if and only if all diagonal maps from that structure into its ultrapowers are isomorphisms. An object A in a category C equipped with ultrapr ...
arXiv:math/0302340v2 [math.AG] 7 Sep 2003
... X is a complete smooth divisor with normal crossings then the weight filtration coincides with the Zeeman filtration given by ”codimension of cycles”. In general there is an inclusion (the terms of the weight filtration are bigger). It is a result of McCrory for hypersurfaces and of F. Guillen ([8]) ...
... X is a complete smooth divisor with normal crossings then the weight filtration coincides with the Zeeman filtration given by ”codimension of cycles”. In general there is an inclusion (the terms of the weight filtration are bigger). It is a result of McCrory for hypersurfaces and of F. Guillen ([8]) ...
Review of metric spaces
... Recall that a metric space X, d is a set X with a metric d(, ), a real-valued function such that, for x, y, z ∈ X, • (Positivity) d(x, y) ≥ 0 and d(x, y) = 0 if and only if x = y • (Symmetry) d(x, y) = d(y, x) • (Triangle inequality) d(x, z) ≤ d(x, y) + d(y, z) A metric space X has a natural topolog ...
... Recall that a metric space X, d is a set X with a metric d(, ), a real-valued function such that, for x, y, z ∈ X, • (Positivity) d(x, y) ≥ 0 and d(x, y) = 0 if and only if x = y • (Symmetry) d(x, y) = d(y, x) • (Triangle inequality) d(x, z) ≤ d(x, y) + d(y, z) A metric space X has a natural topolog ...