Given a map T : X → X on a set X we examine under what conditions there is a separable metrizable or an hereditarily Lindelöf or a Lindelöf topology on X with respect to which T is a continuous map. For separable metrizable and hereditarily Lindelöf, it turns out that there is such a topology precisely when the cardinality of X is no greater than c, the cardinality of the continuum. We go on to...

We obtain several results and examples concerning the general question “When must a space with a small diagonal have a Gδ-diagonal?”. In particular, we show (1) every compact metrizably fibered space with a small diagonal is metrizable; (2) there are consistent examples of regular Lindelöf (even hereditarily Lindelöf) spaces with a small diagonal but no Gδ-diagonal; (3) every first-countable he...

There is a locally compact Hausdorff space which is linearly Lindelöf and not Lindelöf. This answers a question of Arhangel’skii and Buzyakova.

Abstract We consider fractional Schrödinger operators with possibly singular potentials and derive certain spatially averaged estimates for its complex-time heat kernel. The main tool is a Phragmén–Lindelöf theorem polynomially bounded functions on the right complex half-plane. interpolation leads to nonoptimal off-diagonal bounds.

We establish two Phragmén–Lindelöf theorems for a fully nonlinear elliptic equation. consider dynamical boundary condition that includes both spatial variable and time derivative terms. As term, we non-linear Neumann-type operator with strict monotonicity in the normal direction of on term. Our first result is an equation epigraph $$\mathbb {R}^n$$ . Because assume good structural condition, wh...

A subset A of a space X is called regular open if A = IntA, and regular closed if X\A is regular open, or equivalently, if A= IntA. A is called semiopen [16] (resp., preopen [17], semi-preopen [3], b-open [4]) ifA⊂ IntA (resp.,A⊂ IntA,A⊂ IntA ,A⊂ IntA∪ IntA). The concept of a preopen set was introduced in [6] where the term locally dense was used and the concept of a semi-preopen set was introd...

We present a forcing construction of a Hausdorff zero-dimensional Lindelöf space X whose square X is again Lindelöf but its cube X has a closed discrete subspace of size c, hence the Lindelöf degree L(X) = c. In our model the Continuum Hypothesis holds true. After that we give a description of a forcing notion to get a space X such that L(X) = א0 for all positive integers n, but L(X0 ) = c = א2.

We will introduce and study the pairwise weakly regular-Lindelöf bitopological spaces and obtain some results. Furthermore, we study the pairwise weakly regular-Lindelöf subspaces and subsets, and investigate some of their characterizations. We also show that a pairwise weakly regularLindelöf property is not a hereditary property. Some counterexamples will be considered in order to establish so...

Among the various covering properties of topological spaces a lot of attention has been given to those covers which involve open and regularly open sets. In 1982 Balasubramanian [4] introduced and studied the notion of nearly Lindelöf spaces and in 1984 Willard and Dissanayake [21] gave the notion of almost Lindelöf spaces. Then in 1996 Cammaroto and Santoro [5] studied and gave further new res...