scholarly journals Graph topologies on closed multifunctions

2003 ◽  
Vol 4 (2) ◽  
pp. 445 ◽  
Author(s):  
Giuseppe Di Maio ◽  
Enrico Meccariello ◽  
Somashekhar Naimpally

<p>In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.</p>

1971 ◽  
Vol 12 (4) ◽  
pp. 466-472 ◽  
Author(s):  
Vincent J. Mancuso

The concept of simultaneous or collective continuity of a family of single valued functions was introduced by Gale [3] for regular spaces to replace equicontinuiry in metric spaces. Smithson [6] extended the standard point-open and compact-open function space topologies to include multi-valued functions. The aim of this paper is to use these topologies and extend the notion of collective continuity in order to obtain an Ascoli type theorem for multi-valued functions analogous to Theorem 1 in [3, p. 304]. We have the following theorem in mind:


2017 ◽  
Vol 18 (2) ◽  
pp. 331 ◽  
Author(s):  
Ankit Gupta ◽  
Ratna Dev Sarma

<div class="page" title="Page 1"><div class="layoutArea"><div class="column"><p><span>Function space topologies are investigated for the class of continuous multifunctions. Using the notion of continuous convergence, splittingness and admissibility are discussed for the topologies on continuous multifunctions. The theory of net of sets is further developed for this purpose. The (</span><span>τ,μ</span><span>)-topology on the class of continuous multifunctions is found to be upper admissible, while the compact-open topology is upper splitting. The point-open topology is the coarsest topology which is coordinately admissible, it is also the finest topology which is coordinately splitting. </span></p></div></div></div>


1966 ◽  
Vol 9 (3) ◽  
pp. 349-352 ◽  
Author(s):  
Somashekhar Amrith Naimpally

Let X and Y be topological spaces. If Y is a uniform space then one of the most useful function space topologies for the class of continuous functions on X to Y (denoted by C) is the topology of uniform convergence. The reason for this usefulness is the fact that in this topology C is closed in YX (see Theorem 9, page 227 in [2]) and consequently, if Y is complete then C is complete. In this paper I shall show that a similar result is true for the function space of connectivity functions in the topology of uniform convergence and for the function space of semi-connectivity functions in the graph topology when X×Y is completely normal. In a subsequent paper the problem of connected functions will be discussed.


2019 ◽  
Vol 26 (1) ◽  
pp. 125-131
Author(s):  
Alik M. Najafov ◽  
Rena E. Kerbalayeva

Abstract In this paper we introduce a new function space {B_{p,\theta,a,\varkappa,\tau}^{\langle l\rangle}(s,G)} with parameters of many groups of variables of Besov–Morrey type. In view of the embedding theorems we study some properties of the functions which belong to these spaces.


1970 ◽  
Vol 35 (2) ◽  
pp. 381-388 ◽  
Author(s):  
J. Hansard

Sign in / Sign up

Export Citation Format

Share Document