Topological dualities and completions for (distributive) partially ordered sets Luciano J. González
... more general setting, Gehrke and Jónsson [29, 30] studied which identities that are preserved in a distributive lattice expansion (a distributive lattice with additional operations, not necessarily operators) are also preserved in its canonical extension. In their 2001 paper [26], Gehrke and Hardin ...
... more general setting, Gehrke and Jónsson [29, 30] studied which identities that are preserved in a distributive lattice expansion (a distributive lattice with additional operations, not necessarily operators) are also preserved in its canonical extension. In their 2001 paper [26], Gehrke and Hardin ...
Totally supra b−continuous and slightly supra b−continuous functions
... f (x), there exists a supra b-open subset U in X containing x such that f (U ) ⊆ V . The function f is said to be slightly supra b-continuous if it has this property at each point of X. Remark 3.2. Every supra b-continuous function is slightly supra b-continuous but the converse need not be true as ...
... f (x), there exists a supra b-open subset U in X containing x such that f (U ) ⊆ V . The function f is said to be slightly supra b-continuous if it has this property at each point of X. Remark 3.2. Every supra b-continuous function is slightly supra b-continuous but the converse need not be true as ...
Supra b-compact and supra b
... is similar. Suppose that Ũ = {Uα : α ∈ ∆} is a cover of A ∩ B by supra b-open sets in X. Then Õ = {Uα : α ∈ ∆} ∪ {X − B} is a cover of A by supra b-open sets in X, but A is supra b-compact relative to X, so there exist α1 , α2 , ..., αn ∈ ∆ such that A ⊆ (∪{Uαi : i = 1, 2, ..., n}) ∪ (X − B). Then ...
... is similar. Suppose that Ũ = {Uα : α ∈ ∆} is a cover of A ∩ B by supra b-open sets in X. Then Õ = {Uα : α ∈ ∆} ∪ {X − B} is a cover of A by supra b-open sets in X, but A is supra b-compact relative to X, so there exist α1 , α2 , ..., αn ∈ ∆ such that A ⊆ (∪{Uαi : i = 1, 2, ..., n}) ∪ (X − B). Then ...
S-CLUSTER SETS IN FUZZY TOPOLOGICAL SPACES 1. Introduction
... if jsupp()j is nite (resp. jsupp() = 1). A fuzzy set is called quasi-coincident with a fuzzy set ,denoted by q [12], i there exists x 2 X such that (x) + (x) > 1. If is not quasi-coincident with , then we write q. In what follows, we use the concept of a fuzzy topological space (fts ...
... if jsupp()j is nite (resp. jsupp() = 1). A fuzzy set is called quasi-coincident with a fuzzy set ,denoted by q [12], i there exists x 2 X such that (x) + (x) > 1. If is not quasi-coincident with , then we write q. In what follows, we use the concept of a fuzzy topological space (fts ...
SYMMETRIC SPECTRA Contents Introduction 2 1
... of a more general theory of localization of model categories [Hir97]; we have not adopted this approach, but both [Hir97] and [DHK] have influenced us considerably. Symmetric spectra have already proved useful. In [GH97], symmetric spectra are used to extend the definition of topological cyclic homo ...
... of a more general theory of localization of model categories [Hir97]; we have not adopted this approach, but both [Hir97] and [DHK] have influenced us considerably. Symmetric spectra have already proved useful. In [GH97], symmetric spectra are used to extend the definition of topological cyclic homo ...
On soft continuous mappings and soft connectedness of soft
... 3. Soft continuous mappings between soft topological spaces In this section, we will introduce the notion of soft continuous mapping between soft topological spaces and discuss some related properties. Let X, Y be two initial universe sets and E be a non-empty set of parameters. In what follows, th ...
... 3. Soft continuous mappings between soft topological spaces In this section, we will introduce the notion of soft continuous mapping between soft topological spaces and discuss some related properties. Let X, Y be two initial universe sets and E be a non-empty set of parameters. In what follows, th ...
Morphisms of Algebraic Stacks
... Let X = [U/R] be a presentation of an algebraic stack. Then the properties of the diagonal of X over S, are the properties of the morphism j : R → U ×S U . For example, if X = [S/G] for some smooth group G in algebraic spaces over S then j is the structure morphism G → S. Hence the diagonal is not a ...
... Let X = [U/R] be a presentation of an algebraic stack. Then the properties of the diagonal of X over S, are the properties of the morphism j : R → U ×S U . For example, if X = [S/G] for some smooth group G in algebraic spaces over S then j is the structure morphism G → S. Hence the diagonal is not a ...
Title of Paper (14 pt Bold, Times, Title case)
... For easy understanding of the material presented in this paper we recall some basic definitions. For details we refer to [10], [11] and [12]. The fuzzy set on a universe X is a function with domain X and values in I = [0, 1]. The class of all fuzzy sets on X will be denoted by IX and symbols λ, δ, . ...
... For easy understanding of the material presented in this paper we recall some basic definitions. For details we refer to [10], [11] and [12]. The fuzzy set on a universe X is a function with domain X and values in I = [0, 1]. The class of all fuzzy sets on X will be denoted by IX and symbols λ, δ, . ...
Weak forms of S-α-open sets and decompositions of continuity via
... Remark 5.6. The notion of weak G-preopenness (resp. G-β-openness) is independent of the notion of AG -sets (resp. NG -sets) as shown by the following examples. Example 5.7. Let X = {a, b, c, d}, τ = {φ, X, {a}, {b, d}, {a, b, d}} and the grill G = {{d}, {a, d}, {b, d}, {c, d}, {a, d, b}, {b, d, c}, ...
... Remark 5.6. The notion of weak G-preopenness (resp. G-β-openness) is independent of the notion of AG -sets (resp. NG -sets) as shown by the following examples. Example 5.7. Let X = {a, b, c, d}, τ = {φ, X, {a}, {b, d}, {a, b, d}} and the grill G = {{d}, {a, d}, {b, d}, {c, d}, {a, d, b}, {b, d, c}, ...
General Topology - Fakultät für Mathematik
... continuous for every i ∈ I. Consequently, I must contanin all elements of S = i∈I {fi−1 (O)|O ∈ Oi }. Now let O be the topology defined by the subbasis S. Then O is the coarsest topology for which all fi are continuous and by the above I is necessarily finer than O. To finish the proof we show that ...
... continuous for every i ∈ I. Consequently, I must contanin all elements of S = i∈I {fi−1 (O)|O ∈ Oi }. Now let O be the topology defined by the subbasis S. Then O is the coarsest topology for which all fi are continuous and by the above I is necessarily finer than O. To finish the proof we show that ...
NON-HAUSDORFF GROUPOIDS, PROPER ACTIONS AND K
... c : G(0) → R+ is a “cutoff” function (Section 6). Contrary to the Hausdorff case, the function c is not continuous, but it is the restriction to G(0) of a continuous map X 0 → R+ (see above for the definition of X 0 ). The Hilbert module E(G) is one of the ingredients in the definition of the assemb ...
... c : G(0) → R+ is a “cutoff” function (Section 6). Contrary to the Hausdorff case, the function c is not continuous, but it is the restriction to G(0) of a continuous map X 0 → R+ (see above for the definition of X 0 ). The Hilbert module E(G) is one of the ingredients in the definition of the assemb ...