Sequential Cauchy spaces
Sequential characterizations of metrizability
Sequential compactness vs. countable compactness
The general question of when a countably compact topological space is sequentially compact, or has a nontrivial convergent sequence, is studied from the viewpoint of basic cardinal invariants and small uncountable cardinals. It is shown that the small uncountable cardinal 𝔥 is both the least cardinality and the least net weight of a countably compact space that is not sequentially compact, and that it is also the least hereditary Lindelöf degree in most published models. Similar results, some definitive,...
Sequential completeness and -sequential completeness are different
Sequential completeness versus Čech - completeness
Sequential + separable vs sequentially separable and another variation on selective separability
A space X is sequentially separable if there is a countable D ⊂ X such that every point of X is the limit of a sequence of points from D. Neither “sequential + separable” nor “sequentially separable” implies the other. Some examples of this are presented and some conditions under which one of the two implies the other are discussed. A selective version of sequential separability is also considered.
Sequential space methods in general topological spaces
Sequential structures induced by merotopies
Sequential topological groups of any sequential order under CH
For any a countable sequential topological group of sequential order α is constructed using CH.
Sequentially complete spaces
Sequentially determined convergence spaces
Sequentially quotient mappings
Set-theoretic consistency results and topological theorems concerning the normal Moore space conjecture and related problems [Book]
Short proofs of two theorems in topology
We present short and elementary proofs of the following two known theorems in General Topology: (i) [H. Wicke and J. Worrell] A weakly -refinable countably compact space is compact. (ii) [A. Ostaszewski] A compact Hausdorff space which is a countable union of metrizable spaces is sequential.
Sigma-finiteness and regularity of generalized Radon measures.
We extend some known sigma-finiteness and regularity results for (locally finite) Radon measures to locally sigma-finite or locally moderated Radon measures of type (H), and we obtain other new ones. The main result states that the regularity and the sigma-finiteness are equivalent for alllocally moderated, diffused, Radon measures of type (H) in a T1 topological space which is either weakly metacompact or paralindelöf (resp. metalindelöf) and has a concassage of Lindelöf (resp. separable) subsets....
Sixty questions on regular not paracompact spaces
Skeletally Dugundji spaces
We introduce and investigate the class of skeletally Dugundji spaces as a skeletal analogue of Dugundji space. Our main result states that the following conditions are equivalent for a given space X: (i) X is skeletally Dugundji; (ii) every compactification of X is co-absolute to a Dugundji space; (iii) every C*-embedding of the absolute p(X) in another space is strongly π-regular; (iv) X has a multiplicative lattice in the sense of Shchepin [Shchepin E.V., Topology of limit spaces with uncountable...
Skula spaces
Small subsets of first countable spaces
Smooth partitions of unity in preduals of WCG spaces.