SUMS OF QUASICONTINUOUS FUNCTIONS DEFINED ON PSEUDOMETRIZABLE SPACES

1996 ◽  
Vol 22 (1) ◽  
pp. 328 ◽  
Author(s):  
Borsík
Keyword(s):  
Quasicontinuous Functions ◽  
Pseudometrizable Spaces

scholarly journals On countably compact quasi-pseudometrizable spaces

1990 ◽  
Vol 49 (2) ◽  
pp. 231-240 ◽  
Author(s):  
Sergio Salbany ◽  
Salvador Romaguera
Keyword(s):  
Metrizable Space ◽  
Countably Compact ◽  
Pseudometrizable Spaces

AbstractWe prove the following results: (1) A quasi-metrizable space is compact if and only if every compatible quasi-metric has a quasi-metric left d—sequential completion. (2) A quasipseudometrizable space is countably compact if and only if every compatible quasi-pseudometric is pointwise bounded. (3) A quasi-pseudometrizable space is compact if and only if every compatible quasi-pseudometric is precompact.

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).

scholarly journals DARBOUX QUASICONTINUOUS FUNCTIONS

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

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.

Sign in / Sign up

Export Citation Format

Share Document