International Journal of
Advanced Multidisciplinary Application

Volume 2, Issue 11

• Author(s)K.Shaju, Sabu Sebastian, C.P.Santhosh, V.Girish, M.P.Sirajudheen
• AffiliationAssistant Professor,Department of Mathematics,NAM College,Kallikkandy,Kannur ,Kerala,India, Professor,Department of Mathematics, Nirmalagiri College, Kerala,India, Associate Professor,Department of Mathematics,KMM Govt.Wemon’s College,Kannur ,Kerala,India, Associate Professor, Department of Statistics, NAM College, Kallikkandy, Kannur ,Kerala, India, Assistant Professor, Department of Mathematics, Sir Syed College, Thalipparamba, Kannur ,Kerala,India
• Page No.20-23
• Volume, Issue & YearVolume 2, Issue 11, November 25
• Published On2025/11/30
• JournalInternational Journal of Advanced Multidisciplinary Application (IJAMA)
• ISSN No.3048-9350
• DOIhttps://doi.org/10.5281/zenodo.17586928

Article Indexing

Abstract

Several countable minimal dense subsets of R are known to exist. An important example is the set Z+Zq={a+bq: a,b∈Z}, where q is an irrational number.In this paper, we establish an analogous result in the space of matrices 〖 M〗_k (R). We prove that the set
J={A+BT:A,B〖∈M〗_k (Z)} is dense in M_k (R) under the metric on M_k (R) defined by
〖d(X,Y)=‖X-Y‖〗_p= (∑_(1≤i,j≤k)▒|X(i,j)-Y(i,j)|^p )^(1/p)
Where T be a fixed matrix in M_k (R) whose entries are irrational numbers.
Keywords:

Keywords: Dense sets, Space of matrices, Sequential convergence, Archimedean Property, Countability

References

1. [1]. Hardy, G. H., and Wright, E. M. An Introduction to the Theory of Numbers. Oxford
2. University Press, 2008.
3. [2]. Niven, I. Irrational Numbers.The Mathematical Association of America, 1956.
4. [3]. Rudin, W. Principles of Mathematical Analysis. McGraw-Hill, 1976.

Explore Our Related Journals

Looking for the right journal for your next manuscript? Explore our international peer-reviewed journals covering engineering, management, computer science, artificial intelligence and multidisciplinary research.