TY - JOUR
AU - Kohli, J.K.
AU - Singh, D.
AU - Kumar, Rajesh
PY - 2008/10/01
Y2 - 2024/06/24
TI - Generalizations of Z-supercontinuous functions and Dδ-supercontinuous functions
JF - Applied General Topology
JA - Appl. Gen. Topol.
VL - 9
IS - 2
SE -
DO - 10.4995/agt.2008.1804
UR - https://polipapers.upv.es/index.php/AGT/article/view/1804
SP - 239-251
AB - <p>Two new classes of functions, called ‘almost z-supercontinuous functions’ and ’almost D<sub>δ</sub>-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 D<sub>δ</sub>-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 D<sub>δ</sub>-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.</p>
ER -