Applied General Topology - Vol 11, No 1 (2010)https://riunet.upv.es:443/handle/10251/868212022-01-19T20:46:37Z2022-01-19T20:46:37ZOn almost cl-supercontinuous functionsKanibir, A.Reilly, Ivan L.https://riunet.upv.es:443/handle/10251/868272020-10-06T15:33:41Z2017-09-08T11:43:54ZOn almost cl-supercontinuous functions
Kanibir, A.; Reilly, Ivan L.
[EN] Recently the class of almost cl-supercontinuous functions between topological spaces has been studied in some detail. We conside rthis class of functions from the point of view of change(s) of topology. In particular, we conclude that this class of functions coincides with the usual class of continuous functions when the domain and codomain have been retopologized appropriately. Some of the consequences of this fact are considered in this paper.
2017-09-08T11:43:54ZBetween continuity and set connectednessKohli, J.K.Singh, D.Kumar, RajeshAggarwal, Jeetendrahttps://riunet.upv.es:443/handle/10251/868262020-10-06T15:33:41Z2017-09-08T11:41:31ZBetween continuity and set connectedness
Kohli, J.K.; Singh, D.; Kumar, Rajesh; Aggarwal, Jeetendra
[EN] Two new weak variants of continuity called 'R-continuity'and 'F-continuity' are introduced. Their basic properties are studied and their place in the hierarchy of weak variants of continuity, that already exist in the literature, is elaborated. The class of R-continuous functions properly contains the class of continuous functions and is strictly contained in each of the three classes of (1) faintly continu-ous functions studied by Long and Herrignton (Kyungpook Math. J.22(1982), 7-14); (2) D-continuous functions introduced by Kohli (Bull.Cal. Math. Soc. 84 (1992), 39-46), and (3) F-continuous functions which in turn are strictly contained in the class of z-continuous functions studied by Singal and Niemse (Math. Student 66 (1997), 193-210).So the class of R-continuous functions is also properly contained in each of the classes of D∗-continuous functions, D-continuous function and set connected functions.
2017-09-08T11:41:31ZBetween strong continuity and almost continuityKohli, J.K.Singh, D.https://riunet.upv.es:443/handle/10251/868242020-10-06T15:33:41Z2017-09-08T11:39:16ZBetween strong continuity and almost continuity
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).
2017-09-08T11:39:16ZOne point compactification for generalized quotient spacesKarunakaran, V.Ganesan, C.https://riunet.upv.es:443/handle/10251/868232021-11-08T07:57:09Z2017-09-08T11:36:13ZOne point compactification for generalized quotient spaces
Karunakaran, V.; Ganesan, C.
[EN] The concept of Generalized function spaces which were introduced and studied by Zemanian are further generalized as Boehmian spaces or as generalized quotient spaces in the recent literature. Their topological structure, notions of convergence in these space sare also investigated. Some sufficient conditions for the metrizability are also obtained. In this paper we shall assume that a generalized quotient space is non-compact and realize its one point compactification as a quotient space.
2017-09-08T11:36:13ZTopological dynamics on hyperspacesSharma, PuneetNagar, Animahttps://riunet.upv.es:443/handle/10251/868222021-06-18T09:50:10Z2017-09-08T11:34:13ZTopological dynamics on hyperspaces
Sharma, Puneet; Nagar, Anima
[EN] In this paper we wish to relate the dynamics of the base map to the dynamics of the induced map. In the process, we obtain conditions on the endowed hyperspace topology under which the chaotic behaviour of the map on the base space is inherited by the induced map on the hyperspace. Several of the known results come up as corollaries to our results. We also discuss some metric related dynamical properties on the hyperspace that cannot be deduced for the base dynamics.
2017-09-08T11:34:13Z