Related papers: Introduction To Typed Topological Space
Topological statistical theory provides the foundation for a modern mathematical reformulation of classical statistical theory: Structural Statistics emphasizes the structural assumptions that accompany distribution families and the set of…
We introduce strings in metric spaces and define string complexes of metric spaces. We describe the class of 2-dimensional topological spaces which arise in this way from finite metric spaces.
Topological landscape is introduced for networks with functions defined on the nodes. By extending the notion of gradient flows to the network setting, critical nodes of different indices are defined. This leads to a concise and…
In this essay, a general case of information systems contains quantum information systems is considered. By presenting an algorithmic method a new kind of information topology is defined and considered. Continuous maps between two…
By considering nests on a given space, we explore order-theoretical and topological properties that are closely related to the structure of a nest. In particular, we see how subbases given by two dual nests can be an indicator of how close…
We introduce a notion of equivalence on tilings which is formulated in terms of their local structure. We compare it with the known concept of locally deriving one tiling from another and show that two tilings of finite type are…
We use the recently introduced \'etale open topology to prove several facts about large fields. We show that these facts lift to a very general topological setting.
In this thesis, we introduce the subject of D-spaces and some of its most important open problems which are related to well known covering properties. We then introduce a new approach for studying D-spaces and covering properties in…
We define a type system with intersection types for an extension of lambda-calculus with unbind and rebind operators. In this calculus, a term with free variables, representing open code, can be packed into an "unbound" term, and passed…
This brief note gives a survey on results relating to existence of closed points on schemes, including an elementary topological characterization of the schemes with (at least one) closed point.
A new method is given for computing generators of the homology groups with integer coefficients for any finite $T_0$-space. An important role in this method is played by irreducible cycles which are defined here and give rise to continuous…
In this paper we study the property of separability of functional space with the open-point and bi-point-open topologies.
We introduce the notion of the "covering type" of a space, which is more subtle that the notion of Lusternik Schnirelman category. It measures the complexity of a space which arises from coverings by contractible subspaces whose non-empty…
The machinery is suggested to describe the varying spacetime topology on the level of its substitutes by finite topological spaces.
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. Starting from ZFC, the exposition in this first part includes relation and order theory as well as a construction of…
We show that a topometric space $X$ is topometrically isomorphic to a type space of some continuous first-order theory if and only if $X$ is compact and has an open metric (i.e., satisfies that $\{p : d(p,U) < \varepsilon\}$ is open for…
Syntax connects words to each other in very specific ways. Two words are syntactically connected if they depend directly on each other. Syntactic connections usually happen within a sentence. Gathering all those connection across several…
We present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary, one model defined as an inverse limit of spaces of maps between configuration spaces and another which is cosimplicial.…
For a variety over certain topological rings $R$, like $\mathbb{Z}_p$ or $\mathbb{C}$, there is a well-studied way to topologize the $R$-points on the variety. In this paper, we generalize this definition to algebraic stacks. For an…
This paper introduces a model that identifies spatial relationships for a structural analysis based on the concept of simplicial complex. The spatial relationships are identified through overlapping two map layers, namely a primary layer…