Cluster Sets of The Bicomplex Nets

Sukhdev Singh, Sanjeev Kumar

Abstract


This paper initiates the study of clustering of bicomplex nets. Clustering on dierent
types of zones in the bicomplex space have studied. Clustering in idempotent order topology and
idempotent product topology have been compared. Relation between clustering of bicomplex nets
and the clustering of its component nets have been discussed. Finally, investigations have been
made connecting clustering of a bicomplex net and connement of its subnets.


Keywords


06F30; 54A99

References


J Cockle, On the Symbols of Algebra and on the Theory of Tessarines, Philosophical Mag-

azine, 37:3(1849).

G S Dragoni, Sulle funzioni olomorfe di una variabile bicomplessa, Reale Accad. dI-

talia, Mem. Classe Sci. Nat. Mat., 5,(1964).

W R Hamilton, Lectures on Quaternions, Royal Irish Academy, (1853).

G. B. Price, An Introduction to Multicomplex Spaces and Functions, Marcel Dekker Inc.,

New York (1987).

B. J. Pettis, Cluster Sets of Nets, Proc. Amer. Math. Soc., 22(1969), 386-391.

Rajiv K. Srivastava, Bicomplex Numbers: Analysis and Applications, Math. Student,

:1-4(2003), 63-87.

Rajiv K. Srivastava, Certain Topological Aspects of Bicomplex Space, Bull. Pure and

Appl. Math., 2, (2008) 222{234,.

Rajiv K. Srivastava and Sukhdev Singh, Certain Bicomplex Dictionary Order Topolo-

gies, Inter. J. of Math. Sci. and Engg. Appls., 4:III, (2010), 245-258.

Rajiv K. Srivastava and Sukhdev Singh, On Bicomplex Nets and Their Connements,

Amer. J. of Math. and Stat., 1:1, (2011), 8-16,.

C Segre, The Real Representation of Complex Elements and the Hyperalgebraic En-

tities., Math. Ann., 40:1, (1892), 413-467.

N Sampinato, Estensione nel Compo Bicomplesso di Due Teoremi, del LeviCivita e

del Severi, per le Funzione Olomorfe di Due Variablili Complesse, I, II, Atti Reale

Accad. Naz. Lincei, Rend, 22:6(1935), 38-43.

N Sampinato, Sulla Rappresentazione delle Funzioni di Variabile Bicomplessa Total-

mente Derivabili, Ann. Mat. Pura Appl., 14:4, (1936), 305-325.

S. Willard, General Topology, Addison-Wesley Publishing Company, Inc., (1970).


Refbacks

  • There are currently no refbacks.


free counters