Lebesgue Measurability of Separately Continuous Functions and Separability by V. V. Mykhaylyuk

“…A connection between the separability and the countable chain condition of spaces with L-property (a topological space X has L-property if for every topological space Y, separately continuous function f:X×Y→ℝ and open set I⊆ℝ, the set f−1(I) is an Fσ-set) is studied. …”
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Using the Degree r∈[0,1] in Defining Rough Fuzzy Sets by S. H. Alsulami, S. E. Abbas, S. Saleh, Ismail Ibedou

“…This paper introduced a new definition of rough fuzzy sets based on a fuzzy ideal l defined on a fuzzy approximation space X,R. This definition considered the degree r∈0,1 in defining the after sets and the before sets of the arbitrary fuzzy relation R on the finite set of objects X. …”
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On the surjectivity of linear transformations by M. Damlakhi, V. Anandam

“…Let B be a reflexive Banach space, X a locally convex space and T:B→X (not necessarily bounded) linear transformation. …”
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Generalized Exponential Trichotomies for Abstract Evolution Operators on the Real Line by Nicolae Lupa, Mihail Megan

“…We emphasize that we do not assume the invertibility of the evolution operators on the whole space X (unlike the case of evolution operators generated by differential equations).…”
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On G-finitistic spaces and related notions by Satya Deo, Janak Singh Andotra

“…We show that X is G-finitistic iff the orbit space X/G is finitistic. This result allows us to answer a question raised in [5] asking for an equivariant characterization of a non-finitistic G-space where G is a compact Lie group. …”
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The (𝐷) Property in Banach Spaces by Danyal Soybaş

“…We show that the space 𝐿1(𝑣) of real functions, which are integrable with respect to a measure 𝑣 with values in a Banach space 𝑋, has (D) property. We give some other results concerning Banach spaces with (D) property.…”
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A Nonlocal Cauchy Problem for Fractional Integrodifferential Equations by Fang Li, Jin Liang, Tzon-Tzer Lu, Huan Zhu

“…This paper is concerned with a nonlocal Cauchy problem for fractional integrodifferential equations in a separable Banach space X. We establish an existence theorem for mild solutions to the nonlocal Cauchy problem, by virtue of measure of noncompactness and the fixed point theorem for condensing maps. …”
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A Note on Property (gb) and Perturbations by Qingping Zeng, Huaijie Zhong

“…An operator T∈ℬ(X) defined on a Banach space X satisfies property (gb) if the complement in the approximate point spectrum σa(T) of the upper semi-B-Weyl spectrum σSBF+-(T) coincides with the set Π(T) of all poles of the resolvent of T. …”
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Semi-topological properties by Bhamini M. P. Nayar, S. P. Arya

“…In the present paper we prove the following results: (1) A topological property P is semi-topological if and only if the statement (X,𝒯) has P if and only if (X,F(𝒯)) has P′ is true where F(𝒯) is the finest topology on X having the same family of semi-open sets as (X,𝒯), (2) If P is a topological property being minimal P is semi-topological if and only if for each minimal P space (X,𝒯), 𝒯=F(𝒯).…”
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Abelian group in a topos of sheaves: torsion and essential extensions by Kiran R. Bhutani

“…Finally we show that for a first countable hausdorff space X essential extensions of torsion groups in AbSh0(X) are torsion iff X is discrete.…”
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Common fixed point theorems for commuting k-uniformly Lipschitzian mappings by M. Elamrani, A. B. Mbarki, B. Mehdaoui

“…We give a common fixed point existence theorem for any sequence of commuting k-uniformly Lipschitzian mappings (eventually, for k=1 for any sequence of commuting nonexpansive mappings) defined on a bounded and complete metric space (X,d) with uniform normal structure. After that we deduce, by using the Kulesza and Lim (1996), that this result can be generalized to any family of commuting k-uniformly Lipschitzian mappings.…”
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On a Fractional SPDE Driven by Fractional Noise and a Pure Jump Lévy Noise in ℝd by Xichao Sun, Zhi Wang, Jing Cui

“…We study a stochastic partial differential equation in the whole space x∈ℝd, with arbitrary dimension d≥1, driven by fractional noise and a pure jump Lévy space-time white noise. …”
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A Remark on the Stability of Approximative Compactness by Zhenghua Luo, Longfa Sun, Wen Zhang

“…Let Λ be an index set and for every λ∈Λ, let Yλ be a subspace of a Banach space Xλ. For 1≤p<∞, let X=⊕lpXλ and Y=⊕lpYλ. We prove that Y (resp., BY) is approximatively τ-compact in X if and only if, for every λ∈Λ, Yλ (resp., BYλ) is approximatively τ-compact in Xλ.…”
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Topologies on Superspaces of TVS-Cone Metric Spaces by Xun Ge, Shou Lin

“…This paper investigates superspaces 𝒫0(X) and 𝒦0(X) of a tvs-cone metric space (X,d), where 𝒫0(X) and 𝒦0(X) are the space consisting of nonempty subsets of X and the space consisting of nonempty compact subsets of X, respectively. …”
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A Note on tvs-G-Cone Metric Fixed Point Theory by Ing-Jer Lin, Chi-Ming Chen, Chao-Hung Chen, Tien-Ying Cheng

“…For a tvs-G-cone metric space (𝑋,𝐺) and for the family 𝒜 of subsets of X, we introduce a new notion of the tvs-ℋ-cone metric ℋ with respect to G, and we get a fixed result for the 𝒞ℬ𝒲-tvs-G-cone-type function in a complete tvs-G-cone metric space (𝒜,ℋ). …”
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Contra-continuous functions and strongly S-closed spaces by J. Dontchev

“…We call a function f:(X,τ)→(Y,σ) contra-continuous if the preimage of every open set is closed. A space (X,τ) is called strongly S-closed if it has a finite dense subset or equivalently if every cover of (X,τ) by closed sets has a finite subcover. …”
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On r-Generalized Fuzzy ℓ-Closed Sets: Properties and Applications by I. M. Taha

“…In the present study, we introduce and characterize the class of r-generalized fuzzy ℓ-closed sets in a fuzzy ideal topological space X,τ,ℓ in Šostak sense. Also, we show that r-generalized fuzzy closed set by Kim and Park (2002) ⟹r-generalized fuzzy ℓ-closed set, but the converse need not be true. …”
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Farthest Points and Subdifferential in 𝑝-Normed Spaces by S. Hejazian, A. Niknam, S. Shadkam

“…We study the farthest point mapping in a 𝑝-normed space 𝑋 in virtue of subdifferential of 𝑟(𝑥)=sup{‖𝑥−𝑧‖𝑝∶𝑧∈𝑀}, where 𝑀 is a weakly sequentially compact subset of 𝑋. …”
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Generalized Grand Lebesgue Spaces Associated to Banach Function spaces by Alireza Bagheri Salec, Seyyed Mohammad Tabatabaie, Alaa Mahdi Talib Albeka

“…In this paper we introduce the class of grand Lebesgue spaces associated to a Banach function space $X$ by replacing the role of the $L^1$-norm by the norm $\|\cdot\|_X$ in the classical construction of the generalized grand Lebesgue spaces. …”
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The Best Approximation Theorems and Fixed Point Theorems for Discontinuous Increasing Mappings in Banach Spaces by Dezhou Kong, Lishan Liu, Yonghong Wu

“…We prove that Fan’s theorem is true for discontinuous increasing mappings f in a real partially ordered reflexive, strictly convex, and smooth Banach space X. The main tools of analysis are the variational characterizations of the generalized projection operator and order-theoretic fixed point theory. …”
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