Final compactness is not preserved under multiplication of spaces of the form C p (X) Academic Article uri icon

abstract

  • Now we recall here that the LindelSf number s of the space X is the smallest infinite cardinal T such that from each open covering of the space X one can extract a subcovering of cardinality no greater than~; if/(X)=~ 0, then X is called finally compact.. The t~ htness t (X) of the space X is the smallest infinite cardinal 9 such that for x~[A], where x~ X, A~ X,[A] being the closure of A, one can find a B~ A for which x~[B] and IB [~ T. Even for the class of topological groups very little is known in relation to question A. First of all one should mention the theorem on the pseudocompactness of the square of a pseudocompact topological group [2]. A negative result is found in [3]: under the assumption of the continuum hypothesis CH there exists a countably compact, hereditarily separable topological group G (nevertheless of countable tightness) for which the space G• G is not countably compact …

publication date

  • January 1, 1988