Semi-radiality in products.
Separation in sequential spaces under PMEA
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 + 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
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.
Spaces in which compact subsets are closed and the lattice of -topologies on a set
We obtain some new properties of the class of KC-spaces, that is, those topological spaces in which compact sets are closed. The results are used to generalize theorems of Anderson [1] and Steiner and Steiner [12] concerning complementation in the lattice of -topologies on a set .
Strongly sequential spaces.
Strongly sequential spaces
The problem of Y. Tanaka [10] of characterizing the topologies whose products with each first-countable space are sequential, is solved. The spaces that answer the problem are called strongly sequential spaces in analogy to strongly Fréchet spaces.