Electronic Resource
Oxford, UK
:
Blackwell Publishing Ltd
Annals of the New York Academy of Sciences
659 (1992), S. 0
ISSN:
1749-6632
Source:
Blackwell Publishing Journal Backfiles 1879-2005
Topics:
Natural Sciences in General
Notes:
A. R. Bernstein introduced the concept of p-compactness (p∈ω*). Years later, W. W. Comfort defined a (pre)-order ≤C on ω* by p ≤C q iff every q-compact space is p-compact. It is natural to consider the relation ≤GC on ω* given by p≤GC q iff every q-compact topological group is p-compact. It is shown that ≤RK≤C, and ≤GC coincide on the set of weak P-points of ω* (≤RK denotes the Rudin–Keisler order on ω*), and that ≤C and ≤GC have several properties in common, but the question whether ≤C=≤GC still remains unsolved. Some properties of free M-compact groups (M⊆α*) are also studied. In particular, it is shown that if α is a regular infinite cardinal and X is 〈 α-bounded, then X is a closed subspace of the free 〈 α-bounded topological (Abelian) group over X.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1111/j.1749-6632.1992.tb32249.x
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