New characterizations of regular open sets, semi-regular sets, and extremally disconnectedness
No hedgehog in the product?
Assuming OCA, we shall prove that for some pairs of Fréchet -spaces , the Fréchetness of the product implies that is . Assuming MA, we shall construct a pair of spaces satisfying the assumptions of the theorem.
Non-accessible points in extremally disconnected compact spaces I
Non-additivity of the fixed point property for tree-like continua
We investigate the fixed point property for tree-like continua that are unions of tree-like continua. We obtain a positive result if finitely many tree-like continua with the fixed point property have dendrites for pairwise intersections. Using Bellamy's seminal example, we define (i) a countable wedge X̂ of tree-like continua, each having the fpp, and X̂ admitting a fixed-point-free homeomorphism, and (ii) two tree-like continua H and K such that H, K, and H∩ K have the fixed point property, but...
Non-constant continuous mappings of metric or compact Hausdorff spaces
Non-homogeneity of
Nonisomorphic thin-tall superatomic Boolean algebras
Non-normality and relative normality of Niemytzki plane
Non-normality points and nice spaces
J. Terasawa in " are non-normal for non-discrete spaces " (2007) and the author in “On non-normality points and metrizable crowded spaces” (2007), independently showed for any metrizable crowded space that each point of its Čech–Stone remainder is a non-normality point of . We introduce a new class of spaces, named nice spaces, which contains both of Sorgenfrey line and every metrizable crowded space. We obtain the result above for every nice space.
Nonsupercompactness and the reduced measure algebra
Normal P-spaces and the -topology
Not all dyadic spaces are supercompact
Null sequences cellular decompositions of
Numerical invariants of 0-dimensional spaces and their Cartesian multiplication.