scholarly journals Some problems on selections for hyperspace topologies

2004 ◽  
Vol 5 (1) ◽  
pp. 71 ◽  
Author(s):  
Valentin Gutev ◽  
Tsugunori Nogura
Mathematika ◽  
1995 ◽  
Vol 42 (1) ◽  
pp. 67-86 ◽  
Author(s):  
C. Costantini ◽  
S. Levi ◽  
J. Pelant

2004 ◽  
Vol 142 (1-3) ◽  
pp. 245-292 ◽  
Author(s):  
Camillo Costantini ◽  
Ľubica Holá ◽  
Paolo Vitolo

2005 ◽  
Vol 153 (5-6) ◽  
pp. 912-923 ◽  
Author(s):  
G. Di Maio ◽  
Lj.D.R. Kočinac ◽  
E. Meccariello

2008 ◽  
Vol 58 (4) ◽  
Author(s):  
Tanvi Jain ◽  
S. Kundu

AbstractA metric space (X, d) is called an Atsuji space if every real-valued continuous function on (X, d) is uniformly continuous. It is well-known that an Atsuji space must be complete. A metric space (X, d) is said to have an Atsuji completion if its completion ($$ \hat X $$, d) is an Atsuji space. In this paper, we study twelve equivalent (external) characterizations for a metric space to have an Atsuji completion in terms of hyperspace topologies. We also characterize topologically those metrizable spaces whose completions are Atsuji spaces.


1992 ◽  
Vol 162 (1) ◽  
pp. 367-381 ◽  
Author(s):  
Gerald Beer ◽  
Alojzy Lechicki ◽  
Sandro Levi ◽  
Somashekhar Naimpally

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