We study the distribution of zeros of holomorphic Hecke cusp forms in several “thin” sets as the weight, k, tends to infinity. We obtain unconditional results for slowly shrinking (with k) hyperbolic balls. This relies on a new, effective, proof of Rudnick’s theorem and on an effective version of Quantum Unique Ergodicity for holomorphic forms, which we obtain in this paper. In addition, assumi...

Let V be an algebraic variety in Cn . We say that V satisfies the strong Phragmén-Lindelöf property (SPL) or that the classical Phragmén-Lindelöf Theorem holds on V if the following is true: There exists a positive constant A such that each plurisubharmonic function u on V which is bounded above by |z| + o(|z|) on V and by 0 on the real points in V already is bounded by A| Im z|. For algebraic ...

We study the class of first-countable Lindel\"of scattered spaces, or "FLS" spaces. While every $T_3$ FLS space is homeomorphic to a subspace $\mathbb Q$, $T_2$ spaces turns out be surprisingly rich. Our investigation these reveals close ties $Q$-sets, Lusin sets, and their relatives, cardinals $\mathfrak{b}$ $\mathfrak{d}$. Many natural questions about turn independent $\mathsf{ZFC}$. prove th...

A space X is said to be set star-Lindelöf if for each nonempty subset of and collection U open sets in such that ⊆⋃U, there a countable V ⊆ St (⋃V,U). The class spaces lie between the Lindel öf spaces. In this paper, we investigate relationship other related by providing some suitable examples study topological properties

A cardinal λ is called ω-inaccessible if for all µ < λ we have µ ω < λ. We show that for every ω-inaccessible cardinal λ there is a CCC (hence cardinality and cofinality preserving) forcing that adds a hereditarily Lindelöf regular space of density λ. This extends an analogous earlier result of ours that only worked for regular λ. In [1] we have shown that for any cardinal λ a natural CCC forci...

In this paper, a simple proof is given for the following theorem due to Blair [7], Blair-Hager [8] and Hager-Johnson [12]: A Tychonoff space X is z-embedded in every larger Tychonoff space if and only if X is almost compact or Lindelöf. We also give a simple proof of a recent theorem of Bella-Yaschenko [6] on absolute embeddings.

A topological space X is a ΣΣ∗-space provided for every sequence 〈fn〉n=0 of continuous functions from X to R, if the series ∑∞ n=0 |fn| converges pointwise then it converges pseudo-normally. We show that every regular Lindelöf ΣΣ∗-space has Rothberger property. We also construct, under the continuum hypothesis, a ΣΣ∗-subset of R of cardinality continuum.

We prove that a space with a σ-weakly hereditarily closurepreserving sn-network is sn-first countable. As an application of this result, we prove that a Lindelöf space with a σ-weakly hereditarily closurepreserving sn-network is sn-second countable. The above results answer some questions posed by L. Yan. AMS Mathematics Subject Classification (2000): 54D20, 54D65, 54E20, 54E99

We construct locally Lindelöf scattered P-spaces (LLSP spaces, for short) with prescribed widths and heights under different set-theoretic assumptions. prove that there is an LLSP space of width $\omega _1$ height _2$