Related papers: The Topos Of A Connectivity Space
A quick overview of category theory and topos theory including slice categories, monics, epics, isos, diagrams, cones, cocones, limits, colimits, products and coproducts, pushouts and pullbacks, equalizers and coequalizers, initial and…
We show that a functor category whose domain is a colored category is a topos.The topos structure enables us to introduce cohomology of colored categories including quasi-schemoids. If the given colored category arises from an association…
A connected topological space is said to be widely-connected if each of its non-degenerate connected subsets is dense in the entire space. The object of this paper is the construction of widely-connected subsets of the plane. We give a…
In this paper we introduce a new kind of topological space, called 'structured space', which locally resembles various kinds of algebraic structures. This can be useful, for instance, to locally study a space that cannot be globally endowed…
After recalling the definition of connectivity spaces and some of their main properties, a way is proposed to represent finite connectivity spaces by directed simple graphs. Then a connectivity structure is associated to each tame link. It…
A neighborhood homotopy is an equivalence relation on spatial graphs which is generated by crossing changes on the same component and neighborhood equivalence. We give a complete classification of all 2-component spatial graphs up to…
Data describing the three-dimensional structure of physical networks is increasingly available, leading to a surge of interest in network science to explore the relationship between the shape and connectivity of physical networks. We…
The structure of almost topological space is a variation of the concept of topological space. It emerged as a formalization of a quantifier first order not definable from the usual existential and universal operators, named the quantifier…
Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves…
By using the representational power of Chu spaces we define the notion of a generalized topological space (or GTS, for short), i.e., a mathematical structure that generalizes the notion of a topological space. We demonstrate that these…
Every topological space has a Kolmogorov quotient that is obtained by identifying topologically indistinguishable points, that is, points that are contained in exactly the same open sets. In this survey, we look at the relationship between…
We prove that a space whose topological complexity equals 1 is homotopy equivalent to some odd-dimensional sphere. We prove a similar result, although not in complete generality, for spaces X whose higher topological complexity TC_n(X) is…
Complex systems are very often organized under the form of networks where nodes and edges are embedded in space. Transportation and mobility networks, Internet, mobile phone networks, power grids, social and contact networks, neural…
We investigate two approximation relations on a T0 topological space, the n-approximation, and the d-approximation, which are generalizations of the way-below relation on a dcpo. Different kinds of continuous spaces are defined by the two…
If the topology of the universe is compact we show how it significantly changes our assessment of the naturalness of the observed structure of the universe and the likelihood of its present state of high isotropy and near flatness arising…
In this note a notion of generalized topological entropy for arbitrary subsets of the space of all sequences in a compact topological space is introduced. It is shown that for a continuous map on a compact space the generalized topological…
Networks embedded in space can display all sorts of transitions when their structure is modified. The nature of these transitions (and in some cases crossovers) can differ from the usual appearance of a giant component as observed for the…
In this note for a topological group $G$, we introduce a bounded subset of $G$ and we find some relationships of this definition with other topological properties of $G$.
We adapt the study of hyperspaces and function spaces from classical topology to digital topology. We define digital hyperspaces and digital function graphs, and study some of their relationships and graphical properties.
This article gives a conceptual introduction to the topos approach to the formulation of physical theories.