A characterization of pseudocompactness by Prabduh Ram Misra, Vinodkumar

“…It is proved here that a completely regular Hausdorff space X is pseudocompact if and only if for any continuous function f from X to a pseudocompact space (or a compact space) Y, f*ϕ is z-ultrafilter whenever ϕ is a z-ultrafilter on X.…”
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Schwarz-Pick Estimates for Holomorphic Mappings with Values in Homogeneous Ball by Jianfei Wang

“…Let BX be the unit ball in a complex Banach space X. Assume BX is homogeneous. The generalization of the Schwarz-Pick estimates of partial derivatives of arbitrary order is established for holomorphic mappings from the unit ball Bn to BX associated with the Carathéodory metric, which extend the corresponding Chen and Liu, Dai et al. results.…”
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Distance to Spaces of Semicontinuous and Continuous Functions by Carlos Angosto

“…Given a topological space X, we establish formulas to compute the distance from a function f∈RX to the spaces of upper semicontinuous functions and lower semicontinuous functions. …”
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Strict topoligies in non-Archimedean function spaces by A. K. Katsaras

“…Some locally F-convex topologies, on the space Cb(X,E) of all bounded continuous functions from a zero-dimensional topological space X to a non-Archimedean locally F-convex space E, are studied. …”
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Separation ratios of maps between Banach spaces by Rosendal, Christian

“…Under the weak assumption on a Banach space $E$ that $E\oplus E$ embeds isomorphically into $E$, we provide a characterisation of when a Banach space $X$ coarsely embeds into $E$ via a single numerical invariant.…”
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A note on nonfragmentability of Banach spaces by S. Alireza Kamel Mirmostafaee

“…We use Kenderov-Moors characterization of fragmentability to show that if a compact Hausdorff space X with the tree-completeness property contains a disjoint sequences of clopen sets, then (C(X), weak) is not fragmented by any metric which is stronger than weak topology. …”
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On spaces whose nowhere dense subsets are scattered by Julian Dontchev, David Rose

“…The concept was recently used in a decomposition of scatteredness a topological space (X,τ) is scattered if and only if X is α-scattered (= its α-topology is scattered) and N-scattered.…”
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Nowhere dense sets and real-valued functions with closed graphs by Ivan Baggs

“…It is also shown that there exists a countable connected Urysohn space X with the property that no closed and nowhere dense subset of X coincides with the points of discontinuity of a real-valued function on X with a closed graph.…”
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The regular open-open topology for function spaces by Kathryn F. Porter

“…It is then shown that Troo on H(X), the collection of all self-homeomorphisms on a topological space, (X,T), is equivalent to the topology induced on H(X) by a specific quasi-uniformity on X, when X is a semi-regular space.…”
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Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces by Somyot Plubtieng, Rabian Wangkeeree

“…Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T:C→C be an asymptotically quasi-nonexpansive mapping. …”
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Convexities and Existence of the Farthest Point by Z. H. Zhang, C. Y. Liu

“…Under the assumption that Banach space 𝑋 is nearly very convex, we give a sufficient condition that bounded, weakly closed subset of 𝑋 has the farthest points. …”
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Tilings in topological spaces by F. G. Arenas

“…A tiling of a topological space X is a covering of X by sets (called tiles) which are the closures of their pairwise-disjoint interiors. …”
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Note on limits of simply continuous and cliquish functions by Janina Ewert

“…The main result of this paper is that any function f defined on a perfect Baire space (X,T) with values in a separable metric space Y is cliquish (has the Baire property) iff it is a uniform (pointwise) limit of sequence {fn:n≥1} of simply continuous functions. …”
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On Existence and Uniqueness of Solutions of a Nonlinear Integral Equation by M. Eshaghi Gordji, H. Baghani, O. Baghani

“…The purpose of this paper is to study the existence of fixed point for a nonlinear integral operator in the framework of Banach space 𝑋∶=𝐶([𝑎,𝑏],ℝ𝑛). Later on, we give some examples of applications of this type of results.…”
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Norm Attaining Multilinear Forms on 𝐿1(𝝁) by Yousef Saleh

“…Furthermore, the study presents an example of a Banach space 𝑋 in which the set of norm attaining operators from 𝑋 into 𝑋∗ is dense in the space of all bounded linear operators 𝐿(𝑋,𝑋∗). …”
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Weighted Vector-Valued Holomorphic Functions on Banach Spaces by Enrique Jordá

“…We use linearization results on these spaces to get conditions which ensure that a function f defined in a subset A of an open and connected subset U of a Banach space X, with values in another Banach space E, and admitting certain weak extensions in a Banach space of holomorphic functions can be holomorphically extended in the corresponding Banach space of vector-valued functions.…”
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Best Proximity Point Theorems for G,D-Proximal Geraghty Maps in JS-Metric Spaces by Phakdi Charoensawan, Tanadon Chaobankoh

“…We study G,D-proximal Geraghty contractions in a JS-metric space X endowed with graph G. We obtain some best proximity theorems for such contractions. …”
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On the fixed points of affine nonexpansive mappings by Hülya Duru

“…Let K be a closed convex bounded subset of a Banach space X and let T:K→K be a continuous affine mapping. …”
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Fuzzy Normed Linear Spaces Generated By Linear Functionals by Ali Reza Khoddami, Fatemeh Kouhsari

“…For a nonzero normed linear space X, we will define some different classes of fuzzy norms on X generated by linear and bounded linear functionals. …”
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Semi separation axioms and hyperspaces by Charles Dorsett

“…Also, it is shown that for each space (X,T), (S(X),E(X)), (S(X0),E(X0)), and (S(XS0),E(XS0)) are homeomorphic, where (X0,Q(X0)) is the T0-identification space of (X,T) and (XS0,Q(XS0)) is the semi-T0-identification space of (X,T), and that if (X,T) is s-regular and R0, then (S(X),E(X)) is semi-T2.…”
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