An observation for simple expansions.
An up-spectral space need not be -spectral.
Application on local discrete expansion.
Are most measurable functions one-to-one?
Atoms and proximal fineness
Atoms in uniformities
Cardinal inequalities implying maximal resolvability
We compare several conditions sufficient for maximal resolvability of topological spaces. We prove that a space is maximally resolvable provided that for a dense set and for each the -character of at is not greater than the dispersion character of . On the other hand, we show that this implication is not reversible even in the class of card-homogeneous spaces.
Cardinal invariants for κ-box products: weight, density character and Suslin number [Book]
Circle spaces
Completely regular modification and products
Condensations of Cartesian products
We consider when one-to-one continuous mappings can improve normality-type and compactness-type properties of topological spaces. In particular, for any Tychonoff non-pseudocompact space there is a such that can be condensed onto a normal (-compact) space if and only if there is no measurable cardinal. For any Tychonoff space and any cardinal there is a Tychonoff space which preserves many properties of and such that any one-to-one continuous image of , , contains a closed copy...
Connected Hausdorff subtopologies
A non-connected, Hausdorff space with a countable network has a connected Hausdorff-subtopology iff the space is not-H-closed. This result answers two questions posed by Tkačenko, Tkachuk, Uspenskij, and Wilson [Comment. Math. Univ. Carolinae 37 (1996), 825–841]. A non-H-closed, Hausdorff space with countable -weight and no connected, Hausdorff subtopology is provided.
Connections between connected topological spaces on the set of positive integers
In this paper we introduce a connected topology T on the set ℕ of positive integers whose base consists of all arithmetic progressions connected in Golomb’s topology. It turns out that all arithmetic progressions which are connected in the topology T form a basis for Golomb’s topology. Further we examine connectedness of arithmetic progressions in the division topology T′ on ℕ which was defined by Rizza in 1993. Immediate consequences of these studies are results concerning local connectedness of...
Convergence preserving permutations of and Fréchet’s space of permutations of
Convergence with respect to -supported ideals
Corrigendum to “Minimal -spaces are countably compact”
Decomposition of topologies on lattices and hyperspaces [Book]
Discrete subsets in Hausdorff topoligies.
Embedding a topological group into a connected group
It was proved in [HM] that each topological group (G,·,τ) may be embedded into a connected topological group (Ĝ,•,τ̂). In fact, two methods of introducing τ̂ were given. In this note we show relations between them.
Embeddings of lattices in the lattice of topologies