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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 smoothfences are exactly the spaces which are approximated by projective sequencesfrom $\mathcal F_0$. We investigate the combinatorial properties of Hassediagrams of finite partial orders and show that $\mathcal F, \mathcal F_0$ areprojective Fra\"iss\'e families with a common projective Fra\"iss\'e limit. Westudy this limit and characterize the smooth fence obtained as its quotient,which we call a Fra\"iss\'e fence. We show that the Fra\"iss\'e fence is ahighly homogeneous space which shares several features with the Lelek fan, andwe examine the structure of its spaces of endpoints. Along the way we establishsome new facts in projective Fra\"iss\'e theory.

Fences, their endpoints, and projective Fra\"iss\'e theory