Related papers: Some Consequences of Restrictions on Digitally Con…

Topological measures and quasi-linear functionals generalize measures and linear functionals. We define and study deficient topological measures on locally compact spaces. A deficient topological measure on a locally compact space is a set…

Through this paper we will modify some of the results of [1], [5], [15], [28], [29], [31], [32] and consequently give the modified results.

We investigate a quasisymmetrically invariant counterpart of the topological Hausdorff dimension of a metric space. This invariant, called the topological conformal dimension, gives a lower bound on the topological Hausdorff dimension of…

We give some basic properties of strongly topologically transitive, supermixing, and hypermixing maps on general topological spaces. Then we present some other results for which our mappings need to be continuous.

We discuss ways in which tools from topology can be used to derive lower bounds for the circuit complexity of Boolean functions.

We establish optimal results on limits at infinity for functions in fractional Sobolev spaces.

This note deals with certain properties of convex functions. We provide results on the convexity of the set of minima of these functions, the behaviour of their subgradient set under restriction, and optimization of these functions over an…

Characterizations of paracompact finite $C$-spaces via continuous selections are given. We apply these results to obtain some properties of finite $C$-spaces. Factorization theorems and a completion theorem for finite $C$- spaces are also…

We discuss topological versions of the closed graph theorem, where continuity is inferred from near continuity in tandem with suitable conditions on source or target spaces. We seek internal characterizations of spaces satisfying a closed…

In this paper we study the number of finite topologies on an $n$-element set subject to various restrictions.

Transformations of digital spaces preserving local and global topology play an important role in thinning, skeletonization and simplification of digital images. In the present paper, we introduce and study contractions of simple pair of…

In this small paper we bring together various open problems on geometric multidimensional continued fractions.

We study some problems in metric Diophantine approximation over local fields of positive characteristic.

We discuss the experimental consequences of hypothetical time variations of the fundamental constants. We emphasize that from a purely phenomenological point of view, only dimensionless fundamental constants have significance. Two classes…

We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.

In this paper we derive geometric consequences from the presence of a long strand of linear syzygies in the minimal free resolution of a closed scheme in projective space whose homogeneous ideal is generated by quadrics. These consequences…

In this article, we study the higher-power moments of restricted divisor functions. In order to establish our main results, we prove a more general result pertaining to the distribution of solutions to certain multiplicative Diophantine…

We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog…

Some new results about multidimensional Topological Persistence are presented, proving that the discontinuity points of a k-dimensional size function are necessarily related to the pseudocritical or special values of the associated…

The aim of this paper is to discuss some applications of general topology in computer algorithms including modeling and simulation, and also in computer graphics and image processing. While the progress in these areas heavily depends on…