Related papers: Projective Fra\"{i}ss\'{e} limits and generalized …
We continue the study of projective Fra\"iss\'e limits developed by Irwin-Solecki and Panagiotopoulos-Solecki by investigating families of epimorphisms between finite trees and finite rooted trees. Ideas of monotone, confluent, and light…
The following paper has been withdrawn from consideration for publication because there are mistakes. In particular, Theorem 3.9 does not hold. Examples were found of finite trees with monotone epimorphisms which do not amalgamate. Further,…
Motivated by the work of Lov\'asz and Szegedy on the convergence and limits of dense graph sequences, we investigate the convergence and limits of finite trees with respect to sampling in normalized distance. Based on separable real trees,…
We develop the theory of homogeneous Polish ultrametric structures. Our starting point is a Fraisse class of finite structures and the crucial tool is the universal homogeneous epimorphism. The new Fraisse limit is an inverse limit,…
We investigate the projective Fra\"{\i}ss\'e family of finite connected graphs with confluent epimorphisms and the continuum obtained as the topological realization of its projective Fra\"{\i}ss\'e limit. This continuum was unknown before.…
We develop a theory of projective Fraisse limits in the spirit of Irwin- Solecki. The structures here will additionally support dual semantics as in [Sl10, Sl12]. Let Y be a compact metrizable space and let G be a closed subgroup of…
We introduce a new class of compact metrizable spaces, which we call fences, and its subclass of smooth fences. We isolate two families $\mathcal F, \mathcal F_0$ of Hasse diagrams of finite partial orders and show that smooth fences are…
Every countable graph can be built from finite graphs by a suitable infinite process, either adding new vertices randomly or imposing some rules on the new edges. On the other hand, a profinite topological graph is built as the inverse…
We present a construction, called the limit of a tree system of spaces (or, less formally, a tree of spaces). The construction is designed to produce compact metric spaces that resemble fractals, out of more regular spaces, such as closed…
We establish some basic properties of quotients of projective Fra\"iss\'e limits and exhibit some classes of compact metric spaces that are the quotient of a projective Fra\"iss\'e limit of a projective Fra\"iss\'e family in a finite…
We study universal minimal flows of the homeomorphism groups of generalized Wa\.zewski dendrites $W_P$, $P\subset\{3,4,\ldots,\omega\}$. If $P$ is finite, we prove that the universal minimal flow of of the homeomorphism group $H(W_P)$ is…
We develop \emph{Fra\"iss\'e theory}, namely the theory of \emph{Fra\"iss\'e classes} and \emph{Fra\"iss\'e limits}, in the context of metric structures. We show that a class of finitely generated structures is Fra\"iss\'e if and only if it…
We introduce a Fra\"iss\'e theory for abstract Cuntz semigroups akin to the theory of Fra\"iss\'e categories developed by Kubi\'s. In particular, we show that any (Cuntz) Fra\"iss\'e category has a unique Fra\"iss\'e limit which is both…
Limits of graphs were initiated recently in the two extreme contexts of dense and bounded degree graphs. This led to elegant limiting structures called graphons and graphings. These approach have been unified and generalized by authors in a…
We explore the tree limits recently defined by Elek and Tardos. In particular, we find tree limits for many classes of random trees. We give general theorems for three classes of conditional Galton-Watson trees and simply generated trees,…
We study a family of Thompson-like groups built as rearrangement groups of fractals from [BF19], each acting on a Wa\.zewski dendrite. Each of these is a finitely generated group that is dense in the full group of homeomorphisms of the…
This dissertation is about rearrangement groups: a class of groups of homeomorphisms of fractal topological spaces. Introduced in 2019 by J. Belk and B. Forrest, this class generalizes the famous trio of Thompson groups $F$, $T$ and $V$ and…
In this note, we continue to be interested in the relationship that connects the restricted distribution of finitude at the local level of intermediate fields of a purely inseparable extension $K/k$ to the absolute or global finitude of…
The notion of hereditarily equivalent continua is classical in continuum theory with only two known nondegenerate examples (arc, and pseudoarc). In this paper we introduce generically hereditarily equivalent continua, i.e. continua which…
The notion of left convergent sequences of graphs introduced by Lov\' asz et al. (in relation with homomorphism densities for fixed patterns and Szemer\'edi's regularity lemma) got increasingly studied over the past $10$ years. Recently,…