Open mapping theorem for spaces of weakly additive homogeneous functionals

Zaitov, A.
December 2010
Mathematical Notes;Dec2010, Vol. 88 Issue 5/6, p655
Academic Journal
We establish that if X and Y are metric compacta and f: X → Y is a continuous surjective mapping, then the openness of the mapping OH( f): OH( X) → OH( Y) of spaces of weakly additive homogeneous functionals is equivalent to the openness of f.


Related Articles

  • RELATIONS BETWEEN Lp- AND POINTWISE CONVERGENCE OF FAMILIES OF FUNCTIONS INDEXED BY THE UNIT INTERVAL. Laschos, Vaios; Mönch, Christian // Real Analysis Exchange;2013, Vol. 38 Issue 1, p177 

    We construct a variety of mappings from the unit interval I into Lp([0, 1]), 1 ≤ p < ∞, to generalize classical examples of Lp-converging sequences of functions with simultaneous pointwise divergence. By establishing relations between the regularity of the functions in the image of...

  • Existence of Fixed Point Results in G-Metric Spaces. Mustafa, Zead; Shatanawi, Wasfi; Bataineh, Malik // International Journal of Mathematics & Mathematical Sciences;2009, p1 

    The purpose of this paper is to prove the existence of fixed points of contractive mapping defined on G-metric space where the completeness is replaced with weaker conditions. Moreover, we showed that these conditions do not guarantee the completeness of G-metric spaces.

  • Convergence Theorems for Perturbed Mann Iteration of Suzuki Generalized Non-expansive Mappings in Banach Spaces. Dimri, R. C.; Chaukiyal, Shruti; Bhatt, Sandeep // Journal of Advanced Studies in Topology;2013, Vol. 4 Issue 1, p159 

    In the present paper, we prove weak and strong convergence theorems for perturbed Mann iteration of Suzuki generalized non-expansive mapping in uniformly convex Banach spaces. The result obtained in this paper extend and improve the results due to [1].

  • A Strong Convergence Theorem for a Family of Quasi-Φ-Nonexpansive Mappings in a Banach Space. Haiyun Zhou; Xinghui Gao // Fixed Point Theory & Applications;2009, Special section p1 

    The purpose of this paper is to propose a modified hybrid projection algorithm and prove a strong convergence theorem for a family of quasi-Ï•-nonexpansive mappings. The strong convergence theorem is proven in the more general reflexive, strictly convex, and smooth Banach spaces with the...

  • A Hybrid Method for a Countable Family of Multivalued Maps, Equilibrium Problems, and Variational Inequality Problems. Watcharaporn Cholamjiak; Suthep Suantai // Discrete Dynamics in Nature & Society;2010, Special section p1 

    We introduce a new monotone hybrid iterative scheme for finding a common element of the set of common fixed points of a countable family of non expansive multi valued maps, the set of solutions of variational inequality problem, and the set of the solutions of the equilibrium problem in a...

  • BETWEEN ARZELÁ AND WHITNEY CONVERGENCE. Ewert, Janina; Jedrzejewski, Jacek // Real Analysis Exchange;2003/2004, Vol. 29 Issue 1, p257 

    A stronger form of the Arzeá convergence is defined and it is compared to other types of convergence.

  • ON THE CONVERGENCE OF GENERALIZED CONTINUOUS MULTIVALUED MAPPINGS.  // Real Analysis Exchange;2009, Vol. 34 Issue 2, p541 

    The main results presented in this paper concern generalized continuous multivalued mappings. An attempt has been made to formulate sufficient conditions under which convergence of nets of multivalued mappings preserves generalized continuity.

  • TOPOLOGIZING THE DENJOY SPACE BY MEASURING EQUIINTEGRABILITY. Alewine, J. Alan; Schechter, Eric // Real Analysis Exchange;2005/2006, Vol. 31 Issue 1, p23 

    Basic limit theorems for the KH integral involve equiintegrable sets. We construct a family of Banach spaces XΔ whose bounded sets are precisely the subsets of KH[0, 1] that are equiintegrable and pointwise bounded. The resulting inductive limit topology on ⋃Δ XΔ = KH[0, 1] is...

  • IK-CONVERGENCE. Mačaj, Martin; Sleziak, Martin // Real Analysis Exchange;2011/2012, Vol. 37 Issue 1, p177 

    In this paper we introduce IK-convergence which is a common generalization of the IK-convergence of sequences, double sequences, and nets. We show that many results that were shown before for these special cases are true for the IK-convergence, too.


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics