  A Smarandache geometry is a geometry which has at least one Smarandachely
denied axiom(1969), i.e., an axiom behaves in at least two different ways
within the same space, i.e., validated and invalided, or only invalided but in
multiple distinct ways and a Smarandache n-manifold is a n-manifold that
support a Smarandache geometry. Iseri provided a construction for Smarandache
2-manifolds by equilateral triangular disks on a plane and a more general way
for Smarandache 2-manifolds on surfaces, called map geometries was presented by
the author in [9]-[10] and [12]. However, few observations for cases of n>=3
are found on the journals. As a kind of Smarandache geometries, a general way
for constructing dimensional n pseudo-manifolds are presented for any integer
n>=2 in this paper. Connection and principal fiber bundles are also defined on
these manifolds. Following these constructions, nearly all existent geometries,
such as those of Euclid geometry, Lobachevshy-Bolyai geometry, Riemann
geometry, Weyl geometry, Kahler geometry and Finsler geometry, ...,etc., are
their sub-geometries.
