Complexity and Good Spaces

M. Intermont (Kalamazoo College) and J. Strom (Western Michigan University)

intermon@kzoo.edu       jeffrey.strom@wmich.edu

This paper is an exploration of two ideas in the study of closed classes:
the A-complexity of a space X and the notion of good spaces (spaces A for
which C(A) = \overline{C(A)}).  A variety of formulae for the computation
of complexity are given, along with some calculations.  Good spaces are
characterized in terms of the functors CW_A and P_A.  The main result is
a countable upper bound for the complexity with respect to the suspension
of A when A is a good space.