Resolvability of Lindelöf spaces

We prove the ω-resolvability of hereditarily finally compact spaces and the resolvability of Lindelöf spaces whose dispersion character is uncountable.     

Remarks on Completely Regular Lindelöf Reflection of Locales

We prove, under the axiom of countable choice, that the l-ring structure of C(L) of real-valued continuous functions on a locale L determines the completely regular Lindelöf reflection lL of L up to isomorphism. Mathematics Subject Classifications (2000) 54C30, 46E25.Project supported by NSF of China (Grant No. 10271056 and Grant No. 10331011).     

Function Spaces on τ-Corson Compacta and Tightness of Polyadic Spaces

We apply the general theory of -Corson Compact spaces to remove an unnecessary hypothesis of zero-dimensionality from a theorem on polyadic spaces of tightness . In particular, we prove that polyadic spaces of countable tightness are Uniform Eberlein compact spaces.     

The Lindelöf principle in ℂ n

Let D be a bounded domain in ? ⁿ . A holomorphic function f: D → ? is called normal function if f satisfies a Lipschitz condition with respect to the Kobayashi metric on D and the spherical metric on the Riemann sphere ??. We formulate and prove a few Lindelöf principles in the function theory of several complex variables.     

A note on weakly Lindelöf frames

The notion of σ^?-properness of a subset of a frame is introduced. Using this notion, we give necessary and su?cient conditions for a frame to be weakly Lindelöf. We show that a frame is weakly Lindelöf if and only if its semiregularization is weakly Lindelöf. For a completely regular frame L, we introduce a condition equivalent to weak realcompactness based on maximal ideals of the cozero part of L. This enables us to show that every weakly realcompact almost P -frame is realcompact. A new characterization of weakly Lindelöf frames in terms of neighbourhood strongly divisible ideals of ?? is provided. The closed ideals of ?? equipped with the uniform topology are applied to describe weakly Lindelöf frames.     

Some consequences of the Lindelöf conjecture

Suppose that the Lindelöf conjecture is valid in the following quantitative form: $$|\zeta (\frac{1}{2} + it)| \leqslant c_0 |t|^{\varepsilon (|t|)} $$ , where ε(t) is a monotone decreasing function, $\varepsilon (2t) \geqslant \tfrac{1}{2}\varepsilon (t),\varepsilon (t) \geqslant \tfrac{1}{{\sqrt {log t} }}$ . Then it is proved that for |t|≥T₀ the disk $\{ s:|s - \tfrac{1}{2} - it| \leqslant v\} $ contains at most 20v log |t| zeros of ζ(s) if $\tfrac{1}{2} \geqslant v \geqslant \sqrt {\varepsilon (t)} $ . There exists an absolute constant A such that for |t|≥T₁ the disk $\{ s:|s - \tfrac{1}{2} - it| \leqslant A\varepsilon ^{\tfrac{1}{3}} (t)\} $ contains at least one zero of ζ(s). Bibliography: 2 titles.     

A Short Note on the Lindelöf Hypothesis

We obtain a quantitative estimate for the measure of the set of large values of the zeta-function on the critical line which is related to the Lindelöf hypothesis and give its application to extreme values (-results). We also investigate the problem of small values.     

A generalization of the Lindelöf theorem

We present a generalization of the Lindelöf theorem on conditions that should be imposed on the coefficients of the Taylor series of an entire transcendental function ? in order that the relation $ln M_f (r) - \tau r^\rho , r \to \infty , M_f (r) = \max \left\{ {\left| {f(r)} \right|:|z| = r} \right\}$ , be satisfied.     

The one-point Lindelöfication of an uncountable discrete space can be surlindelöf

We prove that the one-point Lindelöfication of a discrete space of cardinality ω ₁ is homeomorphic to a subspace of C _p (X) for some hereditarily Lindelöf space X if the axiom holds.     

Ernst Lindelöf in memoriam

Ohne Zusammenfassung     

Some generalizations of Lindelöf and paracompact spaces

In this paper notions ofm-Lindelöf, meta-m-Lindelöf, para-m-Lindelöf andm-closure preserving property are defined, wherem is any infinite cardinal. The main results are the following:

1. A topological space ism-Lindelöf if and only if it is meta-m-Lindelöf and it ism-Lindelöf in the sense of complete accumulation point.
2. A regular topological space is paracompact if and only if it is para-m-Lindelöf and it hasm-closure preserving property for somem.

     

Some remarks on generalizations of countably compact spaces and Lindelöf spaces

We prove some propositions and present some examples concerning the properties between countably compact and pseudocompact and the properties between Lindelöf and pseudo-Lindelöf.     

A result on monotonically Lindelöf generalized ordered spaces

In this paper, we show that a generalized ordered space representable as the union of two closed monotonically Lindelöf subspaces is monotonically Lindelöf, which partially answers a question [7, Question 2] of Levy and Matveev. In addition, we show that the monotone Lindelöf property is hereditary with respect to open Lindelöf subsets in generalized ordered spaces.     

Solutions of Tikhonov Functional Equations and Applications to Multiplication Operators on Szegö Spaces

We consider a natural representation of solutions for Tikhonov functional equations. This will be done by applying the theory of reproducing kernels to the approximate solutions of general bounded linear operator equations (when defined from reproducing kernel Hilbert spaces into general Hilbert spaces), by using the Hilbert–Schmidt property and tensor product of Hilbert spaces. As a concrete case, we shall consider generalized fractional functions formed by the quotient of Bergman functions by Szegö functions considered from the multiplication operators on the Szegö spaces.     

A broader view of the almost Lindelöf property

By first finding necessary and sufficient conditions for the realcompact coreflection, νL, and the regular Lindelöf coreflection, λL, of a completely regular frame L to be isomorphic, we define a frame L to be almost Lindelöf if it is Lindelöf or λL → L is a one-point extension. This agrees with the condition “νL is Lindelöf and L is realcompact or νL is a one-point extension”, which would be a frame version of what are called almost Lindelöf spaces. Thus, the condition “νX is Lindelöf”, which is added in the definition of almost Lindelöf spaces, serves only to compensate for the lack of the regular Lindelöf reflection in Top, and can be dispensed with by concentrating on the frame \({\mathfrak {O}X}\) instead of the space X.     

On nonlinear analogues of the Phragmen–Lindelöf theorem

For solutions of quasilinear elliptic inequalities containing lower-order derivatives, we obtain estimates of the growth that take into account the geometry of the domain. Corollaries of these results are nonlinear analogues of the Phragmen–Lindelöf theorem.     

An Intrinsic Characterization of Monomorphisms in Regular Lindelöf Locales

We characterize monomorphisms in rLLoc, the category of regular Lindelöf locales. Though somewhat complicated, the characterization is intrinsic in the sense that it refers only to the properties of the morphism itself, rather than to properties of some lifting of it to a distant category.     

On the product of relatively weakly almost Lindelöf subsets

The purpose of this note is to show that there exist two Tychonoff spaces X, Y, a subset A of X and a subset B of Y such that A is weakly almost Lindelöf in X and B is weakly almost Lindelöf in Y, but A × B is not weakly almost Lindelöf in X × Y.     

Measures of Countable Compactness and the Lindelf Property in L-Fuzzy Topological Spaces

In this paper,the concept of countable compactness degree and the concept of Lindelf property degree are defined in L-fuzzy topological spaces by means of implication operator →.Many properties of them are discussed.