Applied General Topology

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Applied General Topology publica artículos de investigación originales relacionados con las interacciones entre la topología general y otras disciplinas matemáticas así como los resultados topológicos con aplicaciones a otras áreas de la ciencia, y el desarrollo de teorías topológicas de importancia para permitir futuras aplicaciones.

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Browsing Applied General Topology by Subject "(almost) z-supercontinuous function"

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    Almost cl-supercontinuous functions
    (Universitat Politècnica de València, 2009-04-01) Kohli, J.K.; Singh, D.
    [EN] Reilly and Vamanamurthy introduced the class of ‘clopen maps’ ( ‘cl-supercontinuous functions’). Subsequently generalizing clopen maps, Ekici defined and studied almost clopen maps( almost cl-supercontinuous functions). Continuing in the spirit of Ekici, here basic properties of almost clopen maps are studied. Behavior of separation axioms under almost clopen maps is elaborated. The interrelations between direct and inverse transfer of topological properties under almost clopen maps are investigated. The results obtained in the process generalize, improve and strengthen several known results in literature including those of Ekici, Singh, and others.
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    Between strong continuity and almost continuity
    (Universitat Politècnica de València, 2010-04-01) Kohli, J.K.; Singh, D.
    [EN] As embodied in the title of the paper strong and weak variants of continuity that lie strictly between strong continuity of Levine and almost continuity due to Singal and Singal are considered. Basic properties of almost completely continuous functions (≡ R-maps) and δ-continuous functions are studied. Direct and inverse transfer of topological properties under almost completely continuous functions and δ-continuous functions are investigated and their place in the hier- archy of variants of continuity that already exist in the literature is out- lined. The class of almost completely continuous functions lies strictly between the class of completely continuous functions studied by Arya and Gupta (Kyungpook Math. J. 14 (1974), 131-143) and δ-continuous functions defined by Noiri (J. Korean Math. Soc. 16, (1980), 161-166). The class of almost completely continuous functions properly contains each of the classes of (1) completely continuous functions, and (2) al- most perfectly continuous (≡ regular set connected) functions defined by Dontchev, Ganster and Reilly (Indian J. Math. 41 (1999), 139-146) and further studied by Singh (Quaestiones Mathematicae 33(2)(2010), 1–11) which in turn include all δ-perfectly continuous functions initi- ated by Kohli and Singh (Demonstratio Math. 42(1), (2009), 221-231) and so include all perfectly continuous functions introduced by Noiri (Indian J. Pure Appl. Math. 15(3) (1984), 241-250).
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    Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functions
    (Universitat Politècnica de València, 2008-10-01) Kohli, J.K.; Singh, D.; Kumar, Rajesh
    [EN] Two new classes of functions, called ‘almost z-supercontinuous functions’ and ’almost Dδ-supercontinuous functions’ are introduced. The class of almost z-supercontinuous functions properly includes the class of z-supercontinuous functions (Indian J. Pure Appl. Math. 33(7), (2002), 1097-1108) as well as the class of almost clopen maps due to Ekici (Acta. Math. Hungar. 107(3), (2005), 193-206) and is properly contained in the class of almost Dδ-supercontinuous functions which in turn constitutes a proper subclass of the class of almost strongly θ-continuous functions due to Noiri and Kang (Indian J. Pure Appl. Math. 15(1), (1984), 1-8) and which in its turn include all δ-continuous functions of Noiri (J. Korean Math. Soc. 16 (1980), 161-166). Characterizations and basic properties of almost z-supercontinuous functions and almost Dδ-supercontinuous functions are discussed and their place in the hierarchy of variants of continuity is elaborated. Moreover, properties of almost strongly θ-continuous functions are investigated and sufficient conditions for almost strongly θ-continuous functions to have u θ-closed (θ-closed) graph are formulated.