Algebraic varieties V are investigated on which the natural analogue of the classical Phragmén-Lindelöf principle for plurisubharmonic functions holds. For a homogeneous polynomial P in three variables it is shown that its graph has this property if and only if P has real coefficients, no elliptic factors, is locally hyperbolic in all real characteristics, and the localizations in these charact...

In this paper, we prove the following statements: (1) There exist a Tychonoff space X and a subspace Y of X such that Y is strongly star-Lindelöf in X and e(Y, X) is arbitrarily large, but X is not star-Lindelöf. (2) There exist a Tychonoff space X and a subspace Y of X such that Y is star-Lindelöf in X, but Y is not strongly star-Lindelöf in X.

Some new results about linearly Lindelöf spaces are given here. It is proved that if X is a space of countable spread and X = Y ∪ Z, where Y and Z are meta-Lindelöf spaces, then X is linearly Lindelöf. Moreover, we give a positive answer to a problem raised by A.V. Arhangel’skii and R.Z. Buzyakova.

In this paper, we prove the following two statements: (1) There exists a discretely absolutely star-Lindelöf Tychonoff space having a regular-closed subspace which is not CCC-Lindelöf. (2) Every Hausdorff (regular, Tychonoff) linked-Lindelöf space can be represented in a Hausdorff (regular, Tychonoff) absolutely star-Lindelöf space as a closed Gδ subspace.

We answer questions of Bennett, Lutzer, and Matveev by showing that any monotonically compact LOTS is metrizable, and any first-countable Lindelöf GO-space is monotoncically Lindelöf. We also show that any compact monotonically Lindelöf space is first-countable, and is metrizable if scattered, and that separable monotonically compact spaces are metrizable.

There is a locally compact Hausdorff space of weight אω which is linearly Lindelöf and not Lindelöf.

In this paper,the spatial behaviors of a nonlinear and a quasi-linear parabolic equations with nonlinear boundary conditions are studied on a half cylinder.Under suitable conditions, we get a various, but closely related forms of Phragmén-Lindelöf principle, and we have proved the smooth solution either fails to exist globally, or when it does exist globally,it must tend asymptotically to zero ...

Various derivative estimates for functions of exponential type in a half-plane are proved in this paper. The reader will also find a related result about functions analytic in a quadrant. In addition, the paper contains a result about functions analytic in a strip. Our main tool in this study is the Schwarz–Pick theorem from the geometric theory of functions. We also use the Phragmén–Lindelöf p...

We obtain from the consistency of the existence of a measurable cardinal the consistency of “small” upper bounds on the cardinality of a large class of Lindelöf spaces whose singletons are Gδ sets. Call a topological space in which each singleton is a Gδ set a points Gδ space. A.V. Arhangel’skii proved that any points Gδ Lindelöf space must have cardinality less than the least measurable cardin...