The covering dimension of product of generalized Sorgenfrey lines
The duality between lattice-ordered monoids and ordered topological spaces.
The -topology on compact spaces
The Gruenhage property, property *, fragmentability, and σ-isolated networks in generalized ordered spaces
We examine the Gruenhage property, property * (introduced by Orihuela, Smith, and Troyanski), fragmentability, and the existence of σ-isolated networks in the context of linearly ordered topological spaces (LOTS), generalized ordered spaces (GO-spaces), and monotonically normal spaces. We show that any monotonically normal space with property * or with a σ-isolated network must be hereditarily paracompact, so that property * and the Gruenhage property are equivalent in monotonically normal spaces....
The ideal and new interval topologies on l-groups
The injective hull and the bc-hull of a topological space.
The Lattice of Kernel Operators and Topological Algebra.
The lattice of topologies of topological -groups
The lattices of topologies on a partially ordered set
The Lower and Upper Topologies as a Bitopology
The monad induced by the hom-functor in the category of topological spaces and its associated Eilenberg-Moore algebras.
The Nachbin compactification via convergence ordered spaces.
The order topology for function lattices and realcompactness.
The product of two ordinals is hereditarily dually discrete
In Dually discrete spaces, Topology Appl. 155 (2008), 1420–1425, Alas et. al. proved that ordinals are hereditarily dually discrete and asked whether the product of two ordinals has the same property. In Products of certain dually discrete spaces, Topology Appl. 156 (2009), 2832–2837, Peng proved a number of partial results and left open the question of whether the product of two stationary subsets of is dually discrete. We answer the first question affirmatively and as a consequence also give...
The shrinking property and the B-property in ordered spaces
The Sorgenfrey plane in dimension theory
The Sorgenfrey topology is a join of orderable topologies
The spaces of ordered lo-proximity
The Suslinian number and other cardinal invariants of continua
By the Suslinian number Sln(X) of a continuum X we understand the smallest cardinal number κ such that X contains no disjoint family ℂ of non-degenerate subcontinua of size |ℂ| > κ. For a compact space X, Sln(X) is the smallest Suslinian number of a continuum which contains a homeomorphic copy of X. Our principal result asserts that each compact space X has weight ≤ Sln(X)⁺ and is the limit of an inverse well-ordered spectrum of length ≤ Sln(X)⁺, consisting of compacta with weight ≤ Sln(X) and...
Tietze's convexity theorey for lattices and semilattices.