We apply elementary substructures to characterize the space Cp(X) for Corsoncompact spaces. As a result, we prove that a compact space X is Corson-compact, if Cp(X) can be represented as a continuous image of a closed subspace of (Lτ ) × Z, where Z is compact and Lτ denotes the canonical Lindelöf space of cardinality τ with one non-isolated point. This answers a question of Archangelskij [2].

The celebrated 100-year old Phragmén-Lindelöf theorem, [15, 16], is a far reaching extension of the maximum modulus theorem for holomorphic functions that in its simplest form can be stated as follows: Theorem 1.1. Let Ω ⊂ C be a simply connected domain whose boundary contains the point at infinity. If f is a bounded holomorphic function on Ω and lim supz→z0 |f(z)| ≤ M at each finite boundary p...

A fundamental problem in analytic number theory is to calculate the maximum size of Lfunctions in the critical strip. For example, the importance of the Lindelöf Hypothesis, which is a consequence of the Riemann Hypothesis, is that it provides at least a crude estimate for the maximum in the case of the Riemann zeta-function. In this paper we use a variety of methods to conjecture the true rate...

Experience shows that there is a strong parallel between metrization theory for compact spaces and for linearly ordered spaces in terms of diagonal conditions. Recent theorems of Gruenhage, Pelant, Kombarov, and Stepanova have described metrizability of compact (and related) spaces in terms of the offdiagonal behavior of those spaces, i.e., in terms of properties of X −∆. In this paper, we show...

We consider minimal graphs $$u = u(x,y) > 0$$ over unbounded domains $$D \subset R^2$$ bounded by a Jordan arc $$\gamma $$ on which . prove sort of reverse Phragmén-Lindelöf theorem showing that if D contains sector $$\begin{aligned} S_{\lambda }=\{(r,\theta )=\{-\lambda /2<\theta<\lambda /2\},\quad \pi <\lambda \le 2\pi , \end{aligned}$$ then the rate growth is at most $$r^{\pi /\lambda }$$