An uncountable family of upper semicontinuous functions F such that the graph of F is homeomorphic to the inverse limit of closed unit intervals with F as the only bonding function

2019 ◽  
Vol 253 ◽  
pp. 25-37
Author(s):  
Boštjan Lemež
Keyword(s):  
Inverse Limit ◽  
Upper Semicontinuous ◽  
Uncountable Family ◽  
Upper Semicontinuous Functions ◽  
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.

A method to derive strong laws of large numbers for random upper semicontinuous functions

2001 ◽  
Vol 53 (3) ◽  
pp. 269-275 ◽  
Author(s):  
Ana Colubi ◽  
J. Santos Domı́nguez-Menchero ◽  
Miguel López-Dı́az ◽  
Ralf Körner
Keyword(s):  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Functions ◽  
Large Numbers ◽  
Semicontinuous Functions

Differentiating random upper semicontinuous functions under the integral sign

Test ◽  
2003 ◽  
Vol 12 (1) ◽  
pp. 241-258 ◽  
Author(s):  
Luis J. Rodríguez-Muñiz ◽  
Miguel López-Díaz ◽  
M. Ángeles Gil
Keyword(s):  
Integral Sign ◽  
Upper Semicontinuous ◽  
Upper Semicontinuous Functions ◽  
Semicontinuous Functions
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