Related papers: Structures generated by the Klein-like topology of…
To a significant extent, the metrical and topological properties of spacetime can be described purely order-theoretically. The $K^+$ relation has proven to be useful for this purpose, and one could wonder whether it could serve as the…
We present some modern theories on the structure of spacetime that can be classified as relational theories in the direction of Leibniz's ontology. In order to analyze the nature of spacetime we consider three levels of knowledge…
It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…
In this paper, we study some topological characteristics of the n-normed spaces. We observe convergence sequences, closed sets, and bounded sets in the n-normed spaces using norms of quotient spaces that will be constructed. These norms…
Shape(-and-scale) spaces - configuration spaces for generalized Kendall-type Shape(-and-Scale) Theories - are usually not manifolds but stratified manifolds. While in Kendall's own case - similarity shapes - the shape spaces are…
A theory of quantum dynamics based on a discrete structure underlying the space time manifold is developed for single particles. It is shown that at the micro domain the interaction of particles with the underlying discrete structure…
Lindel\"of spaces are studied in any basic Topology course. However, there are other interesting covering properties with similar behaviour, such as almost Lindel\"of, weakly Lindel\"of, and quasi-Lindel\"of, that have been considered in…
Some boundedness properties of function spaces (considered as topological groups) are studied.
Spherical manifolds yield cosmic spaces with positive curvature. They result by closing pieces from the sphere used by Einstein for his initial cosmology. Harmonic analysis on the manifolds aims at explaining the observed low amplitudes at…
We investigate the steady-state organisation of active particles residing on an interface. Particle activity induces interface deformations, while the local shape of the interface guides particle movement. We consider multiple species of…
Observational cosmology is on the verge of new discoveries that will change the essence of our world-view. The matter concerns origin of initial conditions and physics of dark matter.
I discuss examples where basic structures from Connes' noncommutative geometry naturally arise in quantum field theory. The discussion is based on recent work, partly collaboration with J. Mickelsson.
We construct a category that classifies compact Hausdorff spaces by their shape and finite topological spaces by their weak homotopy type.
An old branch of mathematics, Topology, has opened the road to the discovery of new phases of matter. A hidden topology in the energy spectrum is the key for novel conducting/insulating properties of topological matter.
In this work, we investigate the geometry and topology of compact Einstein-type manifolds with nonempty boundary. First, we prove a sharp boundary estimate, as consequence we obtain under certain hypotheses that the Hawking mass is bounded…
This paper reviews selected aspects of the growth of cosmological structure, covering the following general areas: (1) expected characteristics of linear density perturbations according to various candidate theories for the origin of…
We start from the well-known form of the interval of the special relativity, stare it, and build up an attempt to implement the causality from it. Some features appear to be new, they involve the mass of the particle and the structure of…
Under the assumption that General Relativity (GR) correctly describes the phenomenology of our Universe, astronomical observations provide compelling evidence that (1) the dynamics of cosmic structure is dominated by dark matter (DM), an…
Given a compact space $K$, we denote by $P(K)$ the space of all Radon probability measures on $K$, equipped with the $weak^\ast$ topology inherited from $C(K)^\ast$. For nonmetrizable compacta $K$ even basic properties of $P(K)$ spaces…
Some possible (re)sources of indeterminism and randomness encountered in physics are enumerated. These gaps in the physical laws, if they exist, could possibly be exploited for dualistic interfaces. We also speculate that physical laws and…