Groupoid Quantales: a non étale setting
... locale with ab = a ∧ b and trivial involution (cf. [12, Lemma II.3.3]). It is immediate to see that every supported quantale is an SG-quantale. Therefore the item 1 of the following proposition shows that the fundamental property of supported quantales mentioned above generalizes to SG-quantales. Ev ...
... locale with ab = a ∧ b and trivial involution (cf. [12, Lemma II.3.3]). It is immediate to see that every supported quantale is an SG-quantale. Therefore the item 1 of the following proposition shows that the fundamental property of supported quantales mentioned above generalizes to SG-quantales. Ev ...
Arithmetic fundamental groups and moduli of curves
... direction, by H. Nakamura, F. Pop, A. Tamagawa, and S. Mochizuki, and others. For example, the conjecture is true for curves over p-adic elds with nonabelian fundamental groups. An exposition on these researches in Japanese is available, and its English translation is to appear [25]. 2.3. Arithmeti ...
... direction, by H. Nakamura, F. Pop, A. Tamagawa, and S. Mochizuki, and others. For example, the conjecture is true for curves over p-adic elds with nonabelian fundamental groups. An exposition on these researches in Japanese is available, and its English translation is to appear [25]. 2.3. Arithmeti ...
A Theorem on Remainders of Topological Groups
... are much more sensitive to the properties of topological groups than the remainders of topological spaces are in general. We continue this line of investigation in this paper and consider the following question: when is some remainder of a topological group G perfect? Some partial results in this di ...
... are much more sensitive to the properties of topological groups than the remainders of topological spaces are in general. We continue this line of investigation in this paper and consider the following question: when is some remainder of a topological group G perfect? Some partial results in this di ...
Completely regular spaces
... A lter space X is called a C space provided that whenever A and B are micromeric in X and x 2 X then we have A ! x and B ! x =) A _ B is micromeric. A convergence space is a C space which satis es the condition: For every micromeric collection A in X there exists x 2 X such that A ! x. The subcateg ...
... A lter space X is called a C space provided that whenever A and B are micromeric in X and x 2 X then we have A ! x and B ! x =) A _ B is micromeric. A convergence space is a C space which satis es the condition: For every micromeric collection A in X there exists x 2 X such that A ! x. The subcateg ...
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.