A space X is cometrizable if X has a coarser metric topology such that each point of X has a neighborhood base of metric closed sets. Most examples in the literature of spaces obtained by modifying the topology of the plane or some other metric space are cometrizable. Assuming the Proper Forcing Axiom (PFA) we show that the following statements are equivalent for a cometrizable space X : (a) X ...

We study three problems which involve the nature of subspaces of the Sorgenfrey Line S. It is shown that no integer power of an uncountable subspace of S can be embedded in a smaller power of S. We review the known results about the existence of uncountable X ⊆ S where X is Lindelöf. These results about Lindelöf powers are quite set-theoretic. A descriptive characterization is given of those su...

We apply and develop an idea of E. van Douwen used to define D-spaces. Given a topological property P , the class P∗ dual to P (with respect to neighbourhood assignments) consists of spaces X such that for any neighbourhood assignment {Ox : x ∈X} there is Y ⊂X with Y ∈P and {Ox : x ∈ Y } =X. We prove that the classes of compact, countably compact and pseudocompact are self-dual with respect to ...

We establish qualitative results of Phragmèn-Lindelöf type for upper semicontinuous viscosity solutions of fully nonlinear partial differential inequalities of the second order in general unbounded domains of IR.

We obtain counterparts of the Lindelöf theorem on types entire functions whose growth is determined by Boutroux proximate order. The results are formulated in terms upper density zeros a function and balance its zeros.

We introduce notions of nearly good relations and N-sticky modulo a relation as tools for proving that spaces are D-spaces. As a corollary to general results about such relations, we show that Cp(X) is hereditarily a D-space whenever X is a Lindelöf Σ-space. This answers a question of Matveev, and improves a result of Buzyakova, who proved the same result for X compact. We also prove that if a ...

We present two companion results: Phragmén–Lindelöf type tight bounds on the minimal possible growth of subharmonic functions with a recurrent zero set, and maximal decay harmonic measure outer boundary coland