Type: Article

Countably compact groups and P-limits

S. Garcia-Ferreira; A. H. Tomita;

Abstract:

For phi not equal M subset of or equal to omega*, a space X is said to be quasi M-compact, if for every sequence (x(n))(n<omega), in X there are p E M and x is an element of X such that for every neighborhood V of x in X, {n < omega) : x(n) is an element ofV} is an element of p. This concept strengthens countable compactness. Assuming p = c, we construct a selective ultrafilter p is an element of omega* and a quasi T(p)-compact topological group G whose square is not countably compact, where T(p) is the type of p in omega*. We also construct, via forcing, a countably compact group which is not quasi M-compact for any M G [omega*]<(2c); and a family of topological groups {G, : a < 211 such that for a subset I of 2(c), Pi(alpha is an element of I) G(alpha) is countably compact if and only if vertical bar I vertical bar < 2(c).