Appendix C: Continuous and Semicontinuous Functions, Minima and Infima

1994 ◽  
pp. 191-199
Keyword(s):  
Semicontinuous Functions

Real Functions, Covers and Bornologies

2021 ◽  
Vol 78 (1) ◽  
pp. 199-214
Author(s):  
Lev Bukovský
Keyword(s):  
Topological Space ◽  
Pointwise Convergence ◽  
Continuous Functions ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Functions ◽  
Covering Properties ◽  
Real Functions ◽  
Topology Of Pointwise Convergence ◽  
Semicontinuous Functions

Abstract The paper tries to survey the recent results about relationships between covering properties of a topological space X and the space USC(X) of upper semicontinuous functions on X with the topology of pointwise convergence. Dealing with properties of continuous functions C(X), we need shrinkable covers. The results are extended for A-measurable and upper A-semimeasurable functions where A is a family of subsets of X. Similar results for covers respecting a bornology and spaces USC(X) or C(X) endowed by a topology defined by using the bornology are presented. Some of them seem to be new.

Sandwich Theorems for Semicontinuous Operators

1992 ◽  
Vol 35 (4) ◽  
pp. 463-474 ◽  
Author(s):  
J. M. Borwein ◽  
M. Théra
Keyword(s):  
Lower Semicontinuous ◽  
Lower Semicontinuous Functions ◽  
Classical Interpolation ◽  
Semicontinuous Functions

AbstractWe provide vector analogues of the classical interpolation theorems for lower semicontinuous functions due to Dowker and to Hahn and Katetov-Tong.

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