<abstract xmlns="http://www.w3.org/1999/xhtml"><p> The algebraic or lattice operations in the classes of cliquish or quasicontinuous functions are well known [Z. Grande: <italic>On the maximal multiplicative</italic><italic>family for the class of quasicontinuous functions</italic>, Real Anal. Exchange <bold>15 </bold>(1989-1990), 437-441, Z. Grande, L. Soltysik: <italic>Some remarks on quasicontinuous</italic><italic>real functions</italic>, Problemy Mat. <bold>10 </bold>(1990), 79-86]. This also pertains to the symmetrical quasicontinuity or symmetrical cliquishness [Z. Grande: <italic>On the maximal</italic><italic>additive and multiplicative families for the quasicontinuities of Piotrowski</italic><italic>and Vallin</italic>, Real Anal. Exchange <bold>32 </bold>(2007), 511-518]. In this article, we examine the superpositions <italic>F</italic>(<italic>f, g</italic>), where <italic>F </italic>is a continuous operation and <italic>f, g </italic>are cliquish (symmetrically cliquish) or <italic>f </italic>is continuous (<italic>f </italic>is symmetrically quasicontinuous with continuous sections) and <italic>g </italic>is quasicontinuous (symmetrically quasicontinuous).</p></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).

Some continuous operations on pairs of cliquish functions

The University of Computer Science and Economics TWP Olsztyn ul. Barczewskiego 11 PL–10-061 Olsztyn POLAND

Institute of Mathematics Kazimierz Wielki University Plac Weyssenhoffa 11 PL–85-072 Bydgoszcz POLAND

Tatra Mountains Mathematical Publications

{"article-title":"Some continuous operations on pairs of cliquish functions"}

The algebraic or lattice operations in the classes of cliquish or quasicontinuous functions are well known [Z. Grande: On the maximal multiplicativefamily for...

Some continuous operations on pairs of cliquish functions

Published Online: Nov 12, 2012

Page range: 15 - 25

DOI: https://doi.org/10.2478/v10127-009-0044-3

Keywords
quasicontinuity, symmetrical quasicontinuity, cliquishness, symmetrical cliquishness, strong quasicontinuity, strong cliquishness, continuous operations, maximal family for operation.

This content is open access.

Some continuous operations on pairs of cliquish functions

Published Online: Nov 12, 2012

Page range: 15 - 25

DOI: https://doi.org/10.2478/v10127-009-0044-3

Keywordsquasicontinuity, symmetrical quasicontinuity, cliquishness, symmetrical cliquishness, strong quasicontinuity, strong cliquishness, continuous operations, maximal family for operation.

This content is open access.

Keywords
quasicontinuity, symmetrical quasicontinuity, cliquishness, symmetrical cliquishness, strong quasicontinuity, strong cliquishness, continuous operations, maximal family for operation.