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

‎In this paper we have introduced new types of sets termed as $omega_{_{gamma_{_mu}}}$-open sets with the help of an operation and a generalized topology‎. ‎We have also defined a notion of $gamma_{_mu}$-Lindel"{o}f spaces and discussed some of its basic properties‎.  

In this paper‎, ‎we prove a dichotomy theorem for remainders in‎ ‎compactifications of paratopological groups‎: ‎every remainder of a ‎paratopological group $G$ is either Lindel"{o}f and meager or‎ ‎Baire‎. Furthermore, ‎we give a negative answer to a question posed in [D‎. ‎Basile and A‎. ‎Bella‎, ‎About remainders in compactifications of homogeneous spaces‎, ‎Comment‎. ‎Math‎. ‎Univ‎. ‎Caroli...

We give an example, which demonstrates that in the situation of Picard-Lindel\"of theorem, Lipschitz condition on right hand side $f(x,y)$ with respect to $y$, cannot be replaced by continuity $y$ for every $x$. show that, our classical Euler method detects only one infinitely many solutions and we outline how latter can adjusted find also other numerically.

The Hardy uncertainty principle says that no function is better localized together with its Fourier transform than the Gaussian. textbook proof of result, as well one original proofs by Hardy, refers to Phragm\'en-Lindel\"of theorem. In this note we first describe connection Schr\"odinger equation, and give a new Hardy's result which based on Liouville related second has been underservedly forg...

In this paper, we prove the smooth cubic moments vanish for Hecke--Maass cusp forms, which gives a new case of random wave conjecture. fact, can polynomial decay moments, while second moment (i.e. QUE) no rate is known unconditionally general forms. The proof bases on various estimates central $L$-values. We Lindel\"of average bound first $\rm GL(3)\times GL(2)$ $L$-functions in short intervals...

The Borel map takes a smooth function to its infinite jet of derivatives (at zero). We study the restriction this ultradifferentiable classes Beurling type in very general setting which encompasses classical Denjoy-Carleman and Braun-Meise-Taylor classes. More precisely, we characterize when image one class covers sequence space another terms two weights that define present independent solution...

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...