In many interesting semi-infinite programming problems, all the constraints
are linear inequalities whose coefficients are analytical functions of a o
ne-dimensional parameter. This paper shows that significant geometrical inf
ormation on the feasible set of these problems can be obtained directly fro
m the given coefficient functions. One of these geometrical properties give
s rise to a general purification scheme for linear semi-infinite programs e
quipped with so-called analytical constraint systems. It is also shown that
the solution sets of such kind of consistent systems form a transition cla
ss between polyhedral convex sets and closed convex sets in the Euclidean s
pace of the unknowns.