The word 'mappings' is correct and usable in written English.
You can use 'mappings' to refer to a process of connecting two or more sets of data. For example, "We used mappings to connect the data sets from both of our software systems".
Although almost nothing else seems to be invariant under projective mappings, one should note that lines are mapped onto lines.
One way to construct accounts of computation that are more restrictive than the simple mapping account is to impose a constraint on acceptable mappings.
The French mathematicians Girard Desargues (1591 1661) and Blaise Pascal (1623 62) took the first significant steps by examining what properties of figures were preserved (or invariant) under perspective mappings.
Manifolds can be complicated, but it turned out that their geometry, and the nature of the functions on them, is largely controlled by their topology, the rather coarse properties invariant under one-to-one continuous mappings.
The resulting reports with their detailed mappings told simple, clear stories about one of nature's most powerful events.
Perhaps his most famous result was his proof (with Sir Michael Atiyah) of the Atiyah-Bott fixed-point theorem, which showed the existence of "fixed points" (stable solutions) to certain types of mathematical mappings and gave a method for determining the number of such fixed points.
There is one more important invariant under projective mappings, known as the cross ratio (see the figure).
In connection with his studies of the work of Hilbert, he discovered the plane translation theorem, which characterizes topological mappings of the Cartesian plane, and the first of his fixed-point theorems, which later became important in the establishment of some fundamental theorems in branches of mathematics such as differential equations and game theory.
Projective geometry, branch of mathematics that deals with the relationships between geometric figures and the images, or mappings, that result from projecting them onto another surface.
Mappings can also be conditional.
The basic idea is to consider Kripke models with distinguished (actual) worlds together with two transfer mappings: h1 from the set of worlds of the class of models M1 of L1 into the class of models M2 of L2, and h2 from the set of worlds of the class of models M2 of L2 into the class of models M1 of L1.
