scholarly journals Quasicontinuous functions associated with a Hunt process

1982 ◽  
Vol 86 (1) ◽  
pp. 133-133 ◽  
Author(s):  
Yves Le Jan
2009 ◽  
Vol 44 (1) ◽  
pp. 15-25
Author(s):  
Zbigniew Grande ◽  
Ewa Strońska

Abstract The algebraic or lattice operations in the classes of cliquish or quasicontinuous functions are well known [Z. Grande: On the maximal multiplicativefamily for the class of quasicontinuous functions, Real Anal. Exchange 15 (1989-1990), 437-441, Z. Grande, L. Soltysik: Some remarks on quasicontinuousreal functions, Problemy Mat. 10 (1990), 79-86]. This also pertains to the symmetrical quasicontinuity or symmetrical cliquishness [Z. Grande: On the maximaladditive and multiplicative families for the quasicontinuities of Piotrowskiand Vallin, Real Anal. Exchange 32 (2007), 511-518]. In this article, we examine the superpositions F(f, g), where F is a continuous operation and f, g are cliquish (symmetrically cliquish) or f is continuous (f is symmetrically quasicontinuous with continuous sections) and g is quasicontinuous (symmetrically quasicontinuous).


1997 ◽  
Vol 23 (2) ◽  
pp. 631 ◽  
Author(s):  
Rosen

2010 ◽  
Vol 60 (4) ◽  
Author(s):  
Dušan Holý ◽  
Ladislav Matejíčka

AbstractIn [HOLÁ, Ľ.—HOLÝ, D.: Pointwise convergence of quasicontinuous mappings and Baire spaces, Rocky Mountain J. Math.] a complete answer is given, for a Baire space X, to the question of when the pointwise limit of a sequence of real-valued quasicontinuous functions defined on X is quasicontinuous. In [HOLÁ, Ľ.—HOLÝ, D.: Minimal USCO maps, densely continuous forms and upper semicontinuous functions, Rocky Mountain J. Math. 39 (2009), 545–562], a characterization of minimal USCO maps by quasicontinuous and subcontinuous selections is proved. Continuing these results, we study closed and compact subsets of the space of quasicontinuous functions and minimal USCO maps equipped with the topology of pointwise convergence. We also study conditions under which the closure of the graph of a set-valued mapping which is the pointwise limit of a net of set-valued mappings, is a minimal USCO map.


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