---
abstract: '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 exactly the spaces which are approximated by projective sequences from ${{\mathcal F}_{0}}$. We investigate the combinatorial properties of Hasse diagrams of finite partial orders and show that ${\mathcal F}, {{\mathcal F}_{0}}$ are projective Fraïssé families with a common projective Fraïssé limit. We study this limit and characterize the smooth fence obtained as its quotient, which we call a [Fraïssé ]{}fence. We show that the [Fraïssé ]{}fence is a highly homogeneous space which shares several features with the Lelek fan, and we examine the structure of its spaces of endpoints. Along the way we establish some new facts in projective Fraïssé theory.'
address:
- |
    Département des Opérations\
    Université de Lausanne\
    Quartier UNIL-Chambronne Bâtiment Anthropole\
    1015 Lausanne\
    Switzerland
- |
    Dipartimento di matematica\
    Università di Genova\
    Via Dodecaneso 35\
    16146 Genova\
    Italy
author:
- Gianluca Basso
- Riccardo Camerlo
title: 'Fences, their endpoints, and projective Fraïssé theory'
---

Introduction
============

In this paper we introduce and begin the study 