Let X and Y be Banach spaces, G an open subset of X. If we denote the closure of G by cl(G), let ƒ be a mapping of cl(G) into Y. For X~ Y and ƒ a compact mapping, Leray and Schauder [9] gave a definition of topological degree for mappings of the form ƒ —ƒ on the open set G over a point a of X whenever (I—f)"^) is a compact subset of G. The Leray-Schauder degree for compact displacements is the ...

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.

The compact, geometrically integrated city can and should replace suburban sprawl as the dominant development pattern in the future. This approach to urban planning and design is well established among proponents of the New Urbanist and Smart Growth movements. However, the more radical scenario I propose in this paper is that the compact city should also replace the high-rise, ultra-high-densit...

here, the concept of electric capacity on finsler spaces is introduced and the fundamentalconformal invariant property is proved, i.e. the capacity of a compact set on a connected non-compact finslermanifold is conformal invariant. this work enables mathematicians and theoretical physicists to become morefamiliar with the global finsler geometry and one of its new applications.

We prove that if (M, g) is a compact locally irreducible Riemannian manifold with nonnegative isotropic curvature, then one of the following possibilities hold: (i) M admits a metric with positive isotropic curvature (ii) (M, g) is isometric to a locally symmetric space (iii) (M, g) is Kähler and biholomorphic to CP n. This is implied by the following two results: (i) Let (M, g) be a compact, l...

The minisuperspace model of a Bianchi Type I universe with compact spatial sections is investigated. The classical solutions are brought onto a form were the difference between compact and infinite spatial sections are manifest. One of the features of the compact case is that it has a non-trivial moduli space. The solution space of the compact Bianchi Type I universe is 10 dimensional whereas t...

in this note we characterize the compact weighted frobenius-perron operator $p$ on $l^1(sigma)$ and determine their spectra. we also show that every weakly compact weighted frobenius-perron operator on $l^1(sigma)$ is compact.