Related papers: Locally small spaces with an application

Topology may be interpreted as the study of verifiability, where opens correspond to semi-decidable properties. In this paper we make a distinction between verifiable properties themselves and processes which carry out the verification…

We describe locally compact groups which are separably categorical metric structures. The paper extends (and corrects) Section 3 of the paper A.Ivanov, "Locally compact groups and continuous logic", arXiv: 1206.5473

We study locally compact group topologies on semisimple Lie groups. We show that the Lie group topology on such a group $S$ is very rigid: every 'abstract' isomorphism between $S$ and a locally compact and $\sigma$-compact group $\Gamma$ is…

We give a simple description of the topology of free topological vector space $\mathbb{V}(X)$ and the topology of the free locally convex space $L(X)$ over a Tychonoff space $X$. The case when $X$ is a pseudocompact space is also…

We classify and investigate locally conformally K\"ahler structures on four-dimensional solvable Lie algebras up to linear equivalence. As an application we can produce many examples in higher dimension, here including lcK structures on…

Basic concepts of higher local fields and topologies on their additive and multiplicative groups are introduced.

Spatial aspects of computation are becoming increasingly relevant in Computer Science, especially in the field of collective adaptive systems and when dealing with systems distributed in physical space. Traditional formal verification…

We compute the compactly supported cohomology of the standard realization of any locally finite building.

The purpose of this paper is twofold. First, we define the new spaces and investigate some topological and structural properties. Also, we compute dual spaces of new spaces which are help us in the characterization of matrix mappings.…

This paper is the first in a series whose goal is to develop a fundamentally new way of constructing theories of physics. The motivation comes from a desire to address certain deep issues that arise when contemplating quantum theories of…

We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…

We propose a framework for the connection between local symmetries of discrete Hamiltonians and the design of compact localized states. Such compact localized states are used for the creation of tunable, local symmetry-induced bound states…

We give an explicit simple construction for classifying spaces of maps obtained as hyperplane projections of immersions. We prove structure theorems for these classifying spaces.

I briefly discuss the construction of a theory of particles with curved momentum space and its consequence, the principle of relative locality.

Developing large-scale distributed applications can be a daunting task. object-based environments have attempted to alleviate problems by providing distributed objects that look like local objects. We advocate that this approach has…

We introduce the notion of localized topological pressure for continuous maps on compact metric spaces. The localized pressure of a continuous potential $\varphi$ is computed by considering only those $(n,\epsilon)$-separated sets whose…

Two simple "simplicial approximation" tricks are invoked to prove basic results involving (co)-homology with local coefficients.

We apply the local removable singularity theorem for minimal laminations and the local picture theorem on the scale of topology to obtain two descriptive results for certain possibly singular minimal laminations of $\mathbb{R}^3$. These two…

We study the topology of metric spaces which are definable in o-minimal expansions of ordered fields. We show that a definable metric space either contains an infinite definable discrete set or is definably homeomorphic to a definable set…

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…