Are initially -compact separable regular spaces compact?
We investigate the question of the title. While it is immediate that CH yields a positive answer we discover that the situation under the negation of CH holds some surprises.
We investigate the question of the title. While it is immediate that CH yields a positive answer we discover that the situation under the negation of CH holds some surprises.
Relations between homomorphisms on a real function algebra and different properties (such as being inverse-closed and closed under bounded inversion) are studied.
A tie-point of compact space is analogous to a cut-point: the complement of the point falls apart into two relatively clopen non-compact subsets. We review some of the many consistency results that have depended on the construction of tie-points of . One especially important application, due to Veličković, was to the existence of nontrivial involutions on . A tie-point of has been called symmetric if it is the unique fixed point of an involution. We define the notion of an almost clopen set...