Semiregular frames
Semitopological properties
Semi-topological properties.
Semi-topological properties
Separable extensions of first countable spaces
Separatedness in constructive topology.
Separating by -sets in finite powers of ω₁
It is known that all subspaces of ω₁² have the property that every pair of disjoint closed sets can be separated by disjoint -sets (see [4]). It has been conjectured that all subspaces of ω₁ⁿ also have this property for each n < ω. We exhibit a subspace of ⟨α,β,γ⟩ ∈ ω₁³: α ≤ β ≤ γ which does not have this property, thus disproving the conjecture. On the other hand, we prove that all subspaces of ⟨α,β,γ⟩ ∈ ω₁³: α < β < γ have this property.
Separating maps and the nonarchimedean Hewitt theorem
Separation axioms as absolute properties under monotone unions in weak topology
Separation axioms, covering properties, and inverse limits generated by developable topological spaces [Book]
Separation axioms for partially ordered convergence spaces.
Separation in sequential spaces under PMEA
Separation properties and n-point topological extensions
Separation properties in Moore spaces
Separation properties of the Wallman ordered compactification.
Sequences of disjoint open sets
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