in this paper, after reviewing some results in minimal space, some new results in this setting are given. we prove a generalized form of the fan-kkm typetheorem in minimal vector spaces. as some applications, the open type of matching theorem and generalized form of the classical kkm theorem in minimal vector spaces are given.

‎it is well known that every (real or complex) normed linear space $l$ is isometrically embeddable into $c(x)$ for some compact hausdorff space $x$‎. ‎here $x$ is the closed unit ball of $l^*$ (the set of all continuous scalar-valued linear mappings on $l$) endowed with the weak$^*$ topology‎, ‎which is compact by the banach--alaoglu theorem‎. ‎we prove that the compact hausdorff space $x$ can ...

in this paper, we introduce the cone normed spaces and cone bounded linear mappings. among other things, we prove the baire category theorem and the banach--steinhaus theorem in cone normed spaces.

In the present paper, we study some properties of fuzzy norm of linear operators. At first the bounded inverse theorem on fuzzy normed linear spaces is investigated. Then, we prove Hahn Banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. Finally the set of all compact operators on these spaces is studied.

We consider the construction of the basic bundle gerbe on SU(n) introduced by Meinrenken and show that it extends to a range of groups with unitary actions on a Hilbert space including U(n), Tn and Up(H), the Banach Lie group of unitaries differing from the identity by an element of a Schatten ideal. In all these cases we give an explicit connection and curving on the basic bundle gerbe and cal...

For an infinitely renormalizable quadratic map fc : z 7→ z 2+c with the sequence of renormalization periods {nm} and the rotation numbers {tm = pm/qm}, we prove that if lim supn−1 m log |pm| > 0, then the Mandelbrot set is locally connected at c. We prove also that if lim sup |tm+1| 1/qm < 1 and qm → ∞, then the Julia set of fc is not locally connected provided c is the limit of corresponding c...

1. The Parameter Space for Cubic Maps 2. Real Cubic Maps as Real Dynamical Systems 3. Complex Cubics: The Connectedness Locus 4. Hyperbolic Components Appendix A. Normal Forms and Curves in Parameter Space Appendix B. Centers of Some Hyperbolic Components Appendix C. Comments on the Figures References This article discusses the dynamics of iterated cubic maps from the real or complex line to it...

An index theory for projective families of elliptic pseudodifferential operators is developed when the twisting, i.e. Dixmier-Douady, class is decomposable in H(X;Z)∪H(X;Z) ⊂ H(X;Z). One of the features of this special case is that the corresponding Azumaya bundle can be realized in terms of smoothing operators. The topological and the analytic index of a projective family of elliptic operators...

convexity theory and duality theory are important issues in math- ematical programming. within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. finally,...