Related papers: Which Topologies induced by order convergences
We investigate the definability (reducts) lattice of the order of integers and describe a sublattice generated by relations 'between', 'cycle', 'separation', 'neighbor', '1-codirection', 'order' and equality'. Some open questions are…
It is shown that a surjective monotone map $X\to Y$ between finite $T_0$-spaces induces a surjective map on homology. As such a map turns out to be a sequence of edge contractions in the Hasse diagram of $X$, followed by a homeomorphism,…
The notion of unboundedly order converges has been recieved recently a particular attention by several authors. The main result of the present paper shows that the notion is efficient and deserves that care. It states that a vector lattice…
We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.
We prove that order convergence on a Boolean algebra turns it into a compact convergence space if and only if this Boolean algebra is complete and atomic. We also show that on an Archimedean vector lattice, order intervals are compact with…
I will discuss recent progress by many people in the program of extending natural topological invariants from manifolds to singular spaces. Intersection homology theory and mixed Hodge theory are model examples of such invariants. The past…
In this article we investigate the topological changes undergone by trajectory networks as a consequence of progressive geographical infiltration. Trajectory networks, a type of knitted network, are obtained by establishing paths between…
We formulate a general approach to higher concurrencies in general and neural codes in particular, and suggest how the higher order aspects may be dealt with in using topology.
Let $(P,\leq)$ be a partially ordered set and let $\tau$ be a compact topology on $P$ that is finer than the interval topology. Then $\tau$ is contained in the order (convergence) topology on $(P,\tau)$. So any Priestley topology is…
The following is an amalgamation of four preprints and some computer programs which together represent the current state of our investigations of higher order links. This investigation was motivated by questions discussed and raised in the…
Different notions for order convergence have been considered by various authors. Associated to every notion of order convergence corresponds a topology, defined by taking as the closed sets those subsets of the poset satisfying that no net…
In this article we first correct a recent misconception about a topology that was suggested by Zeeman as a possible alternative to his Fine topology. This misconception appeared while trying to establish the causality in the ambient…
Starting from filters over the set of indices, we introduce structures in a product of sets where the coordinate sets have the given structures.
The intrinsic connection between lattice theory and topology is fairly well established, For instance, the collection of open subsets of a topological subspace always forms a distributive lattice. Persistent homology has been one of the…
We show that several classes of ordered structures (namely, convex linear orders, layered permutations, and compositions) admit first-order logical limit laws.
Both quantum phase transitions and thermodynamic phase transitions are probably induced by fluctuations, yet the specific mechanism through which fluctuations cause phase transitions remains unclear in existing theories. This paper…
The order topology $\tau_o(P)$ (resp. the sequential order topology $\tau_{os}(P)$) on a poset $P$ is the topology that has as its closed sets those that contain the order limits of all their order convergent nets (resp. sequences). For a…
We study some topological properties of attractors.
In this article, we characterize orders that are level-induced suborders anytime they are induced suborders of a superorder. We also characterize orders that are consecutive level-induced suborders anytime they are level-induced suborders…
We investigate how imposing kinetic restrictions on quantum particles that would otherwise hop freely on a two-dimensional lattice can lead to topologically ordered states. The kinetically constrained models introduced here are derived as a…