On Some Paracompactness%type Properties of Fuzzy Topological
... Arhangel’skiii, and obtain several results about The aim of this paper is to study some them. paracompactness-type properties for fuzzy topoFirst, we give some de…nitions: logical spaces. we prove that these properties are good extensions of others de…ned by A.V.Arkhangel’skii (and studied by S.A. P ...
... Arhangel’skiii, and obtain several results about The aim of this paper is to study some them. paracompactness-type properties for fuzzy topoFirst, we give some de…nitions: logical spaces. we prove that these properties are good extensions of others de…ned by A.V.Arkhangel’skii (and studied by S.A. P ...
Minimal T0-spaces and minimal TD-spaces
... but, this contradicts the minimality of ^~. Therefore, for every two open sets in j?~, one is contained in the other, and by Lemma 2, finite unions of point closures are point closures. To see that the family [~[#]:#eX] is a base for ^ " , we observe that since J?~ is a nested family, [~[x]: xe X] i ...
... but, this contradicts the minimality of ^~. Therefore, for every two open sets in j?~, one is contained in the other, and by Lemma 2, finite unions of point closures are point closures. To see that the family [~[#]:#eX] is a base for ^ " , we observe that since J?~ is a nested family, [~[x]: xe X] i ...
A model structure for quasi-categories
... below. A modern introduction to quasi-categories must note that they also serve as a model for the “homotopy theory of homotopy theories.” In some sense a “homotopy theory” can be regarded as a category with some class of weak equivalences that one would like to formally invert. Any such homotopy th ...
... below. A modern introduction to quasi-categories must note that they also serve as a model for the “homotopy theory of homotopy theories.” In some sense a “homotopy theory” can be regarded as a category with some class of weak equivalences that one would like to formally invert. Any such homotopy th ...
Some Properties of θ-open Sets
... The notions of θ-open subsets, θ-closed subsets and θ-closure where introduced by Veličko [14] for the purpose of studying the important class of H-closed spaces in terms of arbitrary fiberbases. Dickman and Porter [2], [3], Joseph [9] and Long and Herrington [11] continued the work of Veličko . R ...
... The notions of θ-open subsets, θ-closed subsets and θ-closure where introduced by Veličko [14] for the purpose of studying the important class of H-closed spaces in terms of arbitrary fiberbases. Dickman and Porter [2], [3], Joseph [9] and Long and Herrington [11] continued the work of Veličko . R ...
Extremally Disconnectedness in Ideal Bitopological Spaces
... topological spaces. A bitopological space (X, τ1, τ2) is a nonempty set X equipped with two topologies τ1 and τ2. The concept of ideal topological spaces was initiated by Kuratowski [17] and Vaidyanathaswamy [29]. An Ideal I on a topological space (X, τ) is a non empty collection of subsets of X whi ...
... topological spaces. A bitopological space (X, τ1, τ2) is a nonempty set X equipped with two topologies τ1 and τ2. The concept of ideal topological spaces was initiated by Kuratowski [17] and Vaidyanathaswamy [29]. An Ideal I on a topological space (X, τ) is a non empty collection of subsets of X whi ...
Basic Category Theory
... We say a functor F preserves a property P if whenever an object or arrow (or. . . ) has P , its F -image does so. Now a functor does not in general preserve monos or epis: the example of Mon shows that the forgetful functor Mon → Set does not preserve epis. An epi f : A → B is called split if there ...
... We say a functor F preserves a property P if whenever an object or arrow (or. . . ) has P , its F -image does so. Now a functor does not in general preserve monos or epis: the example of Mon shows that the forgetful functor Mon → Set does not preserve epis. An epi f : A → B is called split if there ...
SOFT TOPOLOGICAL QUESTIONS AND ANSWERS M. Matejdes
... Consequently, many results from the soft set theory are consequences of the topological results. Any topological notion can be introduced for a soft topological space by direct reformulation. For example, a soft topological space (A, X, τ ) is soft compact (soft normal, soft Baire, soft metrizable a ...
... Consequently, many results from the soft set theory are consequences of the topological results. Any topological notion can be introduced for a soft topological space by direct reformulation. For example, a soft topological space (A, X, τ ) is soft compact (soft normal, soft Baire, soft metrizable a ...
General Topology
... A proof very similar to the following can also be found in Wade (Theorem 10.16). Proof Suppose that V is closed, and let (xn ) be a sequence in V converging to some point x ∈ X. We must show that x ∈ V . Suppose for a contradiction that x ∈ X \ V . Since X \ V is open in X, there is some ε > 0 such ...
... A proof very similar to the following can also be found in Wade (Theorem 10.16). Proof Suppose that V is closed, and let (xn ) be a sequence in V converging to some point x ∈ X. We must show that x ∈ V . Suppose for a contradiction that x ∈ X \ V . Since X \ V is open in X, there is some ε > 0 such ...