Related papers: Limiting Sets for Digital Cones and Suspensions

We study the consequences of some restrictions on digitally continuous functions. One of our results modifies easily to yield an analogous result for topological spaces.

We define cone structures and asymptotic invariants for multigraded systems of ideals, and show that essentially the only restrictions on such structures is convexity, which is imposed formally.

Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.

Digital nets (in base $2$) are the subsets of $[0,1]^d$ that contain the expected number of points in every not-too-small dyadic box. We construct sets that contain almost the expected number of points in every such box, but which are…

We study how the properties of irreducibility and rigidity in digital images interact with Cartesian products, wedges, and cold and freezing sets.

Topological condensed matter systems from class A and class AII of the classification table have received classical electromagnetic and mechanical analogs and protected wave-guiding with such systems has been demonstrated experimentally.…

The concept of $typed$ $topology$ is introduced. In a typed topological space, some open sets are assigned "types", and topological concepts such as closure, connectedness can be defined using types. A finite data set in $R^2$ is a…

Topological defects are found in a variety of systems, and their existence are robust under perturbations due to their topological nature. Here we introduce a new type of topological defects found in electromagnetic waves: topological spin…

We define the finest order on inductive limits of ordered cones which makes the linear mappings monotone and gives rise to the definition of inductive limit topologies for cones. Using the polars of neighborhoods, we establish embeddings…

The concepts of exterior and boundary in multiset topological space are introduced. We further established few relationships between the concepts of boundary, closure, exterior and interior of an M- set. These concepts have been pigeonholed…

This paper introduces semiopen and semiclosed soft sets in soft topological spaces. The notions of interior and closure are generalized using these sets. A detail study is carried out on properties of semiopen, semiclosed soft sets, semi…

We describe the limits of canonical series along families of curves degenerating to a nodal curve which is general for its topology, in the weak sense that the branches over nodes on each of its components are in general position. We define…

Here we look at (collections of) semimetrics and seminorms, including their ultrametric versions. In particular, we are concerned with geometric properties related to connectedness and topological dimension 0.

Using digital topology approach, we construct digital models of closed surfaces as the intersection graphs of LCL covers of the surfaces. It is proved that digital models of closed surfaces are digital 2-dimensional surfaces preserving the…

We present some complexity results concerning the problems of covering a graph with $p$ convex sets and of partitioning a graph into $p$ convex sets. The following convexities are considered: digital convexity, monophonic convexity,…

Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases,…

We construct and classify, in the case of two complex dimensions, the possible tangent cones at points of limit spaces of non-collapsed sequences of K\"ahler-Einstein metrics with cone singularities.

A coordinate cone in R^n is an intersection of some coordinate hyperplanes and open coordinate half-spaces. A semi-monotone set is a defnable in an o-minimal structure over the reals, open bounded subset of R^n such that its intersection…

The purpose of this paper is to construct topology on vague soft sets. The concept of vague soft topology is introduced and its basic properties are given.

We study the dispersion of digital $(0,m,2)$-nets; i.e. the size of the largest axes-parallel box within such point sets. Digital nets are an important class of low-discrepancy point sets. We prove tight lower and upper bounds for certain…