FURTHER DECOMPOSITIONS OF â-CONTINUITYI 1 Introduction
... Definition 2.1. A subset A of an ideal topological space (X, τ , I) is said to be an ∗ g-I-LC∗ -set if A = C ∩ D, where C is ∗ g-open and D is ∗-closed. Proposition 2.2. Let (X, τ , I) be an ideal topological space and A ⊆ X. Then the following hold: 1. If A is ∗ g-open, then A is an ∗ g-I-LC∗ -set; ...
... Definition 2.1. A subset A of an ideal topological space (X, τ , I) is said to be an ∗ g-I-LC∗ -set if A = C ∩ D, where C is ∗ g-open and D is ∗-closed. Proposition 2.2. Let (X, τ , I) be an ideal topological space and A ⊆ X. Then the following hold: 1. If A is ∗ g-open, then A is an ∗ g-I-LC∗ -set; ...
On Maps and Generalized Λb-Sets
... since for the g.Λb -set {b} of (Y, σ), the inverse image f −1 ({b}) = {b} is not a g.Λb-set of (X, τ ). Theorem 3.6. A map f : (X, τ ) → (Y, σ) is g.Λb-irresolute (resp. g.Λb continuous) if and only if, for every g.Λb-set A (resp. closed set A) of (Y, σ) the inverse image f −1 (A) is a g.Vb -set of ...
... since for the g.Λb -set {b} of (Y, σ), the inverse image f −1 ({b}) = {b} is not a g.Λb-set of (X, τ ). Theorem 3.6. A map f : (X, τ ) → (Y, σ) is g.Λb-irresolute (resp. g.Λb continuous) if and only if, for every g.Λb-set A (resp. closed set A) of (Y, σ) the inverse image f −1 (A) is a g.Vb -set of ...
Proper actions on topological groups: Applications to quotient spaces
... It turns out that each tubular set with a compact slicing subgroup is a twisted product. The tubular neighborhood G(S) is G-homeomorphic to the twisted product G ×K S; namely the map ξ : G ×K S → G(S) defined by ξ([g, s]) = gs is a G-homeomorphism (see [15, Ch. II, Theorem 4.2]). In what follows we ...
... It turns out that each tubular set with a compact slicing subgroup is a twisted product. The tubular neighborhood G(S) is G-homeomorphic to the twisted product G ×K S; namely the map ξ : G ×K S → G(S) defined by ξ([g, s]) = gs is a G-homeomorphism (see [15, Ch. II, Theorem 4.2]). In what follows we ...
On upper and lower ω-irresolute multifunctions
... interior of A with respect to τ, respectively. Recently, as generalization of closed sets, the notion of ω-closed sets were introduced and studied by Hdeib [9]. A point x ∈ X is called a condensation point of A if for each U ∈ τ with x ∈ U, the set U ∩ A is uncountable. A is said to be ω-closed [9] ...
... interior of A with respect to τ, respectively. Recently, as generalization of closed sets, the notion of ω-closed sets were introduced and studied by Hdeib [9]. A point x ∈ X is called a condensation point of A if for each U ∈ τ with x ∈ U, the set U ∩ A is uncountable. A is said to be ω-closed [9] ...
Various Notions of Compactness
... It is apparent from the above theorem that countably compact implies limit point compact. The converse is true only in T1 space. On the other hand, this theorem also tell us that countably compact is implied by the next notion of compactness. Definition 5 (Sequentially Compact) K ⊆ X is sequentially ...
... It is apparent from the above theorem that countably compact implies limit point compact. The converse is true only in T1 space. On the other hand, this theorem also tell us that countably compact is implied by the next notion of compactness. Definition 5 (Sequentially Compact) K ⊆ X is sequentially ...
Three Questions on Special Homeomorphisms on Subgroups of $ R
... Question 1.3. Let G be a subgroup of R and let f : G → G be a single fixedpoint involution. Is it true that there exists a binary operation ⊕f on G such that G′ = hG, ⊕f , i is topologically isomorphic to G and f is taking the additive inverse in G′ ? Re-formulation of Question 1.3 Let G be a subgro ...
... Question 1.3. Let G be a subgroup of R and let f : G → G be a single fixedpoint involution. Is it true that there exists a binary operation ⊕f on G such that G′ = hG, ⊕f , i is topologically isomorphic to G and f is taking the additive inverse in G′ ? Re-formulation of Question 1.3 Let G be a subgro ...
