The Zariski topology on the set of semistar operations on an integral
... with the set inclusion, then we can see that properties (i), (iii) and (iv) from Proposition 0.1.9 (called extensivity, idempotency and order preservance, respectively) make sense in any partially ordered set. Therefore the set closure is used as the prototype to define the so called closure operati ...
... with the set inclusion, then we can see that properties (i), (iii) and (iv) from Proposition 0.1.9 (called extensivity, idempotency and order preservance, respectively) make sense in any partially ordered set. Therefore the set closure is used as the prototype to define the so called closure operati ...
Aalborg University - VBN
... (2’) given h : X → U B with hfi = U h̄i , h̄i : Ai → B for each i ∈ I then h = U h̄ for a unique h̄ : A → B. 3.1. Example. (1) A preordered set (A, ≤) is a set A equipped with a reflexive and transitive relation ≤. It means that it satisfies the formulas (∀x)(x ≤ x) and (∀x, y, z)(x ≤ y ∧ y ≤ z → x ...
... (2’) given h : X → U B with hfi = U h̄i , h̄i : Ai → B for each i ∈ I then h = U h̄ for a unique h̄ : A → B. 3.1. Example. (1) A preordered set (A, ≤) is a set A equipped with a reflexive and transitive relation ≤. It means that it satisfies the formulas (∀x)(x ≤ x) and (∀x, y, z)(x ≤ y ∧ y ≤ z → x ...
Semi-quotient mappings and spaces
... papers [7–9]. In this paper we continue the study of properties of s-topological and irresolute-topological groups. Keeping in mind the existing concepts, semi-quotient topology on a set is defined as a generalization of the quotient topology for spaces and groups. Various results on semi-quotients ...
... papers [7–9]. In this paper we continue the study of properties of s-topological and irresolute-topological groups. Keeping in mind the existing concepts, semi-quotient topology on a set is defined as a generalization of the quotient topology for spaces and groups. Various results on semi-quotients ...
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.