  We show that a simple 2D electron system on a square lattice with hoping
between more than nearest neighbors exhibits in the presence of electron spin
exchange interaction properties strikingly similar to those observed in the
underdoped cuprates It is a normal state pseudogap, its behaviour with doping
and T, a form of the spectrum around (0,\pi) etc. The motor is the electronic
topological transition which due to two-dimensionality gets new features with
respect to well-studied 3D case.
