Multiset ideal topological spaces and local functions.


In this article we have introduced the notion of multiset local function on an ideal topological space using the the concept of q-neighbourhood in a multiset topological space. Some basic properties of local functions on multisets have been investigated in multiset ideal topological space.

Biografía del autor

Karishma Shravan, Institute of Advanced Study in Science and Technology.
Mathematical Sciences Division.
Binod Chandra Tripathy, Tripura University.
Department of Mathematics.


W. D. Blizard, Multiset Theory, Notre Dame Journal of Formal Logic, 30 (1), pp. 36-66, (1989).

W. D. Blizard, The development of multiset theory, Modern Logic, 1 (4), pp. 319-352, (1991).

S. El-Sheikh, R. Omar , M. Raafat , Separation Axioms on Multiset Topology, Journal of New Theory, 7, pp. 11-21, (2015).

S. El-Sheikh, Rajab Omar, Mahmoud Raafat, Separation Axioms on Multiset Topology, Journal of New Theory , 7, pp. 11-21, (2015).

S. A. El-Sheikh, R. A-K. Omar, and, M. Raafat, Operators on multiset bitopological spaces, South Asian Jour. Math., 6 (1), pp. 1-9, (2016).

K. P. Girish and S. J. John, Rough multiset and its multiset topology In: Transactions on Rough Sets XIV, Springer; Berlin, Heidelberg. Vol. 6600, Lecture Notes in Computer Science, pp. 62-80, (2011).

K. P. Girish andS. J. John , On Multiset Topologies, Theory Appl. Math. Comput. Sci., 2, pp. 37-52, (2012).

D. Jankovic and T. R. Hamlen, New topologies from old via ideals, Amer. Math. Monthly 97, pp. 295-310, (1990).

A. Kandia, O. A. Tantawy, S. A. El-Sheikh, A. Zakaria , Multiset proximity spaces, Jour. Egyptian Math. Soc., 24, pp. 562-567, (2016).

K. Kuratowski, Topologie I, Warszawa, (1933).

P. M. Mahalakshmi, P. Thangavelu, M-Connectedness in M-Topology, Internat. Jour. Pure Appl. Math., 106 (8), pp. 21-25, (2016).

K. Shravan and B. C. Tripathy, Generalized closed sets in multiset topological space, Proyecciones J. Math., (Accepted for Publication).

B. C. Tripathy and S. Acharjee, On (γ, δ)-Bitopological semi-closed set via topological ideal, Proyecciones J. Math. , 33 (3), pp. 245-257, (2014).

B. C. Tripathy and A. J. Dutta, Lacunary I-convergent sequences of fuzzy real numbers, Proyecciones J. Math. , 34 (3), pp. 205-218, (2015).

B. C. Tripathy and B. Hazarika, I-convergent sequence spaces associated with multiplier sequence spaces, Math. Ineq. Appl., 11 (3), pp. 543-548, (2008).

B. C. Tripathy andB. Hazarika , I-monotonic and I-convergent sequences, Kyungpook Math. J., 51 (2), pp. 233-239, (2011).

B. C. Tripathy ; B. Hazarika and B. Choudhary, Lacunary I-convergent sequences, Kyungpook Math. J. , 52 (4), pp. 473-482, (2012).

B. C. Tripathy and S. Mahanta, On I-acceleration convergence of sequences, Jour. Franklin Inst., 347, pp. 591-598, (2010).

B. C. Tripathy and G. C. Ray, Mixed fuzzy ideal topological spaces, Appl. Math. Comput., 220, pp. 602-607, (2013).

Vaidyanathaswamy, R., Set Topology, (Chelsea, New York), (1960).

A. Zakaria, S. J. John andS. A. El-Sheikh , Generalized rough multiset via multiset ideals, Jour. Intel. Fuzzy Syst., 30, pp. 1791-1802, (2016).

Cómo citar
K. Shravan y B. Tripathy, «Multiset ideal topological spaces and local functions»., PJM, vol. 37, n.º 4, pp. 699-711, nov. 2018.