Homotopy Characterization of ANR Function Spaces

Smrekar, Jaka
January 2013
Journal of Function Spaces & Applications;2013, p1
Academic Journal
Let Y be an absolute neighbourhood retract (ANR) for the class of metric spaces and let X be a topological space. Let YX denote the space of continuous maps from X to Y equipped with the compact open topology. We show that if X is a compactly generated Tychonoff space and Y is not discrete, then YX is an ANR for metric spaces if and only if X is hemicompact and YX has the homotopy type of a CW complex.


Related Articles

  • Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces. Karapinar, Erdal // Fixed Point Theory & Applications;Dec2011, Vol. 2011 Issue 1, p1 

    In this article, lower semi-continuous maps are used to generalize Cristi-Kirk's fixed point theorem on partial metric spaces. First, we prove such a type of fixed point theorem in compact partial metric spaces, and then generalize to complete partial metric spaces. Some more general results are...

  • On a Continuity Theorem for Constructive Functions. Vladimirov, A. // Journal of Mathematical Sciences;May2014, Vol. 199 Issue 1, p6 

    We prove that any everywhere defined constructive mapping from a compact metric space into a complete metric space that preserves the precompactness of subsets is uniformly continuous. Bibliography: 8 titles.

  • PRE-IMAGE ENTROPY FOR MAPS ON NONCOMPACT TOPOLOGICAL SPACES. LEI LIU // Acta Mathematica Universitatis Comenianae;2013, Vol. 82 Issue 2, p219 

    We propose a new definition of pre-image entropy for continuous maps on noncompact topological spaces, investigate fundamental properties of the new pre-image entropy, and compare the new pre-image entropy with the existing ones. The defined pre-image entropy generates that of Cheng and...

  • Relative Topological Entropy of Continuous Functions on Compact Topological Spaces. Asadian, Mohamad Hosein; Ebrahimzadeh, Abolfazl // Global Journal of Pure & Applied Mathematics;2013, Vol. 9 Issue 4, p335 

    In this paper, we introduce a new type of topological entropy of a continuous function on compact space with open covers, and investigate several of its properties. We also express the relationship between this new concept of topological entropy and the classic topological entropy [10].

  • (m;m')-Weakly open maps. Rosas, Ennis; Rajesh, Neelamegarajan; Carpintero, Carlos // Journal of Advanced Research in Pure Mathematics;2010, Vol. 2 Issue 1, p43 

    In this article the concept of (m;m')-weakly b-open maps are introduced and some of their basic properties are obtained; its relationships with other maps are studied. we also study whether the images (resp. the inverse images) of m-b-open, m-b-compact, m-b-connected sets are preserved by these...

  • On Minimal γ-open Set. Hussain, Sabir; Ahmad, Bashir // European Journal of Pure & Applied Mathematics;2009, Vol. 2 Issue 3, p338 

    In this paper, we introduce and discuss minimal γ-open sets in topological spaces. We establish some basic properties of minimal γ-open sets and provide an example to illustrate that minimal γ-open sets are independent of minimal open sets introduced and discussed in [3]. We obtain some...

  • Sβ-paracompact Spaces. Khalaf, Alias B.; Ahmed, Nehmat K. // Journal of Advanced Studies in Topology;2013, Vol. 4 Issue 1, p40 

    In this paper we introduce a new class of space called Sβ-paracompact space and study their properties and characterizations. We also establish the relationship between Sβ-paracompact spaces and other well-known spaces.

  • PRE-TOPOLOGICAL SPACE. Bahan, Reema; Pandey, R. N. // Bulletin of Pure & Applied Sciences-Mathematics;Jul-Dec2012, Vol. 31E Issue 2, p257 

    We give a modified definition of a pre-topological space which is a generalization of a topological space and give a few examples.

  • Points of joint continuity and large oscillations. Maslyuchenko, V.; Nesterenko, V. // Ukrainian Mathematical Journal;Dec2010, Vol. 62 Issue 6, p916 

    For topological spaces X and Y and a metric space Z, we introduce a new class $ \mathcal{N}\left( {X \times Y,\,Z} \right) $ of mappings f: X × Y → Z containing all horizontally quasicontinuous mappings continuous with respect to the second variable. It is shown that, for each mapping...


Read the Article


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

Try another library?
Sign out of this library

Other Topics