In this paper, the notion of βS∗−compactness is introduced in L−fuzzy topological spaces based on S∗−compactness. A βS∗−compactness L-fuzzy set is S∗−compactness and also β−compactness. Some of its properties are discussed. We give some characterizations of βS∗−compactness in terms of pre-open, regular open and semi-open L−fuzzy set. It is proved that βS∗−compactness is a good extension of β−co...

This is a survey on the convergence theory developed rst by Cheeger and Gromov. In their theory one is concerned with the compactness of the class of riemannian manifolds with bounded curvature and lower bound on the injectivity radius. We explain and give proofs of almost all the major results, including Anderson's generalizations to the case where all one has is bounded Ricci curvature. The e...

Compactness and closedness are some of the important properties for studying topological spaces. Several types of these concepts (semi-compactness, pre-compactness, β-compactness,. . ., S-closedness, H-closedness, etc) occur in the literature. In this paper, we applied concept of φ operation which defined by Csaszar [8] to unify and generalized several characterizations and properties of lots o...

In this paper, some characterizations of fuzzifying strong compactness are given, including characterizations in terms of nets and pre -subbases. Several characterizations of locally strong compactness in the framework of fuzzifying topology are introduced and the mapping theorems are obtained.

We extend the pseudoholomorphic curve methods from Floer theory to infinite-dimensional phase spaces and use our results prove existence of a forced time-periodic solution general Hamiltonian PDE with regularizing nonlinearity. In particular, when nonlinearity is sufficiently regularizing, bounded time-periodic, we an version Gromov-Floer compactness by using ideas Diophantine approximations ov...

In this paper, using pre-semi-open L-sets and their inequality, a new notion of PS-compactness is introduced in L-topological spaces, where L is a complete De Morgan algebra. This notion does not depend on the structure of the basis lattice L and L does not need any distributivity.

We study locally compact, geodesically complete, CAT $$(\kappa )$$ spaces ( $$\hbox {GCBA}^\kappa $$ -spaces). prove a Croke-type local volume estimate only depending on the dimension of these spaces. show that doubling condition, with respect to natural measure, implies pure-dimensionality. Then we consider -spaces satisfying uniform packing condition at some fixed scale $$r_0$$ or arbitrarily...

We introduce a new perspective on the classical Nirenberg problem of understanding possible Gauss curvatures metrics $S^{2}$ conformal to round metric. A key tool is employ smooth Cheeger–Gromov compactness theorem obtain general and essentially sharp priori estimates for $K$ contained in naturally defined stable regions. prove that such regions, map $u \to K_{g}$, $g = e^{2u}g_{+1}$ proper Fre...

in this paper, countable compactness and the lindel¨of propertyare defined for l-fuzzy sets, where l is a complete de morgan algebra. theydon’t rely on the structure of the basis lattice l and no distributivity is requiredin l. a fuzzy compact l-set is countably compact and has the lindel¨ofproperty. an l-set having the lindel¨of property is countably compact if andonly if it is fuzzy compact. ...