FUZZY PSEUDOTOPOLOGICAL HYPERGROUPOIDS 1
... As the hyperoperation ”·” is a mapping from H × H to P ∗ (H) giving topologies on H and P ∗ (H) we can speak about the continuity of ”·”. Unfortunately, if a topology is given on H, there is no standard straightforward way of generating a topology on P ∗ (H). This leads to the following definition. ...
... As the hyperoperation ”·” is a mapping from H × H to P ∗ (H) giving topologies on H and P ∗ (H) we can speak about the continuity of ”·”. Unfortunately, if a topology is given on H, there is no standard straightforward way of generating a topology on P ∗ (H). This leads to the following definition. ...
Introduction to Topological Groups
... Section 7 is dedicated to specific properties of the (locally) compact groups used essentially in these notes. The most important property we recall in §7.1 is the open mapping theorem. In §7.2 we recall (with complete proofs) the structure of the closed subgroups of Rn as well as the description of ...
... Section 7 is dedicated to specific properties of the (locally) compact groups used essentially in these notes. The most important property we recall in §7.1 is the open mapping theorem. In §7.2 we recall (with complete proofs) the structure of the closed subgroups of Rn as well as the description of ...
1. Introduction - Departamento de Matemática
... that every point of A is an accumulation point of A. If a ∈ A is not an accumulation point of A, {a} must be in each base for the open sets of A. The set B := {(a, b) ∩ A : a, b ∈ A} ∪ {[c, d) ∩ A : c, d ∈ A and (∃δ > 0) (c − δ, c) ∩ A = ∅} ∪ {(e, f ] ∩ A : e, f ∈ A and (∃δ > 0) (f, f + δ) ∩ A = ∅} ...
... that every point of A is an accumulation point of A. If a ∈ A is not an accumulation point of A, {a} must be in each base for the open sets of A. The set B := {(a, b) ∩ A : a, b ∈ A} ∪ {[c, d) ∩ A : c, d ∈ A and (∃δ > 0) (c − δ, c) ∩ A = ∅} ∪ {(e, f ] ∩ A : e, f ∈ A and (∃δ > 0) (f, f + δ) ∩ A = ∅} ...
On a fuzzy topological structure
... of openess of the union of any crisp family of fuzzy sets should be not less than the "smallest" degree of openess of these sets. The last,axiom (3) .just states, that the empty set and the whole space are "absolutely open". The main examples of fuzzy spaces considered in this paper are the so calle ...
... of openess of the union of any crisp family of fuzzy sets should be not less than the "smallest" degree of openess of these sets. The last,axiom (3) .just states, that the empty set and the whole space are "absolutely open". The main examples of fuzzy spaces considered in this paper are the so calle ...
Unique equilibrium states for flows and homeomorphisms with non
... theorem: expansivity, the specification property, and regularity of the potential. Instead of asking for specification and regularity to hold globally, we ask for these properties to hold on a suitable collection of orbit segments G. Instead of asking for expansivity to hold globally, we ask that al ...
... theorem: expansivity, the specification property, and regularity of the potential. Instead of asking for specification and regularity to hold globally, we ask for these properties to hold on a suitable collection of orbit segments G. Instead of asking for expansivity to hold globally, we ask that al ...
General Topology - Fakultät für Mathematik
... Both trace and product topology are characterized as being the coarsest topology with respect to which certain maps (inclusions, projections) are continuous. In this section we will generalize this construction principle by means of so-called universal properties (as we have already encountered in 1 ...
... Both trace and product topology are characterized as being the coarsest topology with respect to which certain maps (inclusions, projections) are continuous. In this section we will generalize this construction principle by means of so-called universal properties (as we have already encountered in 1 ...
Aspects of topoi
... how such can be replaced with an elementary definition - usually, indeed, with an essentially algebraic definition. The translation from representability to elementary is the Mac Lane-notion of "universal element". For cartesian-closedness (forgive, oh Muse, but "closure" is just not right) we obtai ...
... how such can be replaced with an elementary definition - usually, indeed, with an essentially algebraic definition. The translation from representability to elementary is the Mac Lane-notion of "universal element". For cartesian-closedness (forgive, oh Muse, but "closure" is just not right) we obtai ...
Dynamical characterization of C
... every open neighborhood V of y the set {n ∈ N : T n y ∈ V } has positive upper Banach density and (y, y) belongs the orbit closure of (x, y) in the product system (X × X, T × T ), and an open neighborhood U of y such that F = {n ∈ N : T n x ∈ U}, Central sets have substantial combinatorial contents. ...
... every open neighborhood V of y the set {n ∈ N : T n y ∈ V } has positive upper Banach density and (y, y) belongs the orbit closure of (x, y) in the product system (X × X, T × T ), and an open neighborhood U of y such that F = {n ∈ N : T n x ∈ U}, Central sets have substantial combinatorial contents. ...
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.