scholarly journals DARBOUX QUASICONTINUOUS FUNCTIONS

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

scholarly journals Some continuous operations on pairs of cliquish functions

2009 ◽  
Vol 44 (1) ◽  
pp. 15-25
Author(s):  
Zbigniew Grande ◽  
Ewa Strońska
Keyword(s):  
Continuous Operation ◽  
Quasicontinuous Functions ◽  
Real Functions ◽  
Real Anal

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).

Quasicontinuous functions, minimal usco maps and topology of pointwise convergence

2010 ◽  
Vol 60 (4) ◽  
Author(s):  
Dušan Holý ◽  
Ladislav Matejíčka
Keyword(s):  
Pointwise Convergence ◽  
Rocky Mountain ◽  
Set Valued Mapping ◽  
Upper Semicontinuous Functions ◽  
Quasicontinuous Functions ◽  
Minimal Usco Map ◽  
Pointwise Limit ◽  
Topology Of Pointwise Convergence ◽  
Semicontinuous Functions

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.

scholarly journals Quasicontinuous functions and the topology of uniform convergence on compacta

Filomat ◽  
2021 ◽  
Vol 35 (3) ◽  
pp. 911-917
Author(s):  
Lubica Holá ◽  
Dusan Holý
Keyword(s):  
Topological Space ◽  
Uniform Convergence ◽  
Continuous Functions ◽  
Hausdorff Topological Space ◽  
Cardinal Invariants ◽  
Weight Density ◽  
Quasicontinuous Functions

Let X be a Hausdorff topological space, Q(X,R) be the space of all quasicontinuous functions on X with values in R and ?UC be the topology of uniform convergence on compacta. If X is hemicompact, then (Q(X,R), ?UC) is metrizable and thus many cardinal invariants, including weight, density and cellularity coincide on (Q(X,R), ?UC). We find further conditions on X under which these cardinal invariants coincide on (Q(X,R), ?UC) as well as characterizations of some cardinal invariants of (Q(X,R), ?UC). It is known that the weight of continuous functions (C(R,R), ?UC) is ?0. We will show that the weight of (Q(R,R), ?UC) is 2c.

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