In this paper, we prove new pinching theorems for the first eigenvalue λ1(M) of the Laplacian on compact hypersurfaces of the Euclidean space. These pinching results are associated with the upper bound for λ1(M) in terms of higher order mean curvatures Hk. We show that under a suitable pinching condition, the hypersurface is diffeomorpic and almost isometric to a standard sphere. Moreover, as a...

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.

In this paper, we introduce the concept of rarely generalized regular fuzzy continuous functions in the sense of A.P. Sostak's and Ramadan is introduced. Some interesting properties and characterizations of them are investigated. Also, some applications to fuzzy compact spaces are established.