  In aperiodic order, non-periodic but "ordered" objects such as tilings,
Delone sets, functions and measures are investigated. In this article we depict
the common structure of these objects by using the general framework of
abstract pattern spaces. In particular, using the common structure we define
local matching topology and uniform structure for objects such as tilings in
quite a general space and a symmetry group. We prove Hausdorff property of the
topology and the completeness of the uniform structure under a mild assumption.
We also prove finite local complexity implies the compactness of the continuous
hull and often the converse holds.
