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This work provides a systematic study of the variational properties of decomposable functions which are compositions of an outer support function and an inner smooth mapping under certain constraint qualifications. A particular focus is put…
In this paper, we introduce and explore a new class of topological spaces termed as SC*-normal spaces, defined via SC*-open sets. The concept of SC*-normality is analyzed in relation to classical notions such as normal spaces and g-normal…
We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of P(\omega) with the Cantor set topology.
We construct a family of closeness functions on the space of finite volume Lorentzian geometries using the abundance of discrete intervals in the underlying random causal sets. Although strictly weaker than a Lorentzian Gromov-Hausdorff…
The area of research called \textquotedblleft Lineability\textquotedblright% \ looks for linear structures inside exotic subsets of vector spaces. In the last decade lineability/spaceability has been investigated in rather general settings;…
We present a construction of the soft $T_{0}$ reflection of a soft topological space and characterize some separation axioms developed through the soft $T_{0}$ reflection.
We define covering and separation numbers for functions. We investigate their properties, and show that for some classes of functions there is exact equality of separation and covering. We provide analogues for various geometric…
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
In this article we introduce Variable exponent Fock spaces and study some of their basic properties such as the boundedness of evaluation functionals, density of polynomials, boundedness of a Bergman-type projection and duality.
For an arbitrary field $K$ and $K$-variety $V$, we introduce the \'etale-open topology on the set $V(K)$ of $K$-points of $V$. This topology agrees with the Zariski topology, Euclidean topology, or valuation topology when $K$ is separably…
In this article, we present a twisted version of strong openness property in $L^p$ with applications.
In this paper we study differentiability properties of the map $T\mapsto\phi(T)$, where $\phi$ is a given function in the disk-algebra and $T$ ranges over the set of contractions on Hilbert space. We obtain sharp conditions (in terms of…
We study topological boundedness of order-to-topology bounded and order-to-topology continuous operators from ordered vector spaces to topological vector spaces. The uniform boundedness principle for such operators is investigated.
We study the topological dynamics by iterations of a piecewise continuous, non linear and locally contractive map in a real finite dimensional compact ball. We consider those maps satisfying the "separation property": different continuity…
We show that there is a compact topological space carrying a measure which is not a weak* limit of finitely supported measures but is in the sequential closure of the set of such measures. We construct compact spaces with measures of…
The combinatorial properties of partitions with various restrictions on their hooksets are explored. A connection with numerical semigroups extends current results on simultaneous s/t-cores. Conditions that suffice for a partition to…
We study some topological properties of maximal ideal spaces of certain algebras of almost periodic functions. Our main result is that such spaces are contractible. We present certain corollaries of this result.
A new class of functions called L-fuzzy weakly Semi-Preopen (Semi-Preclosed) functions in L-fuzzy topological spaces are introduced in this paper. Some characterizations of this class and its properties and the relationship with other…
In this work, we Extend Pawlak approximation spaces by topological spaces. Also, Rough Membership, equality and inclusion relations are extended using topological near open sets. In addition, new extended measures of accuracy and quality of…
We use topological methods to study complexity of deep computations and limit computations. We use topology of function spaces, specifically, the classification Rosenthal compacta, to identify new complexity classes. We use the language of…