8 papers
Quotient structure of ultrafilters
Manoranjan Singha, Rohan Pradhan
For ultrafilters u,v on N, the operation u/v is introduced and formalised which acts as quotient-like structures when v strongly divides u.Central to our study is the characterizat…
Exhibition of piecewise syndetic and broken IP sets near idempotent
Ujjal Kumar Hom, Manoranjan Singha
Characterizations of ultrafilters belong to the smallest ideal of Stone-Čech compactification of a discrete semigroup are exhibited using syndetic sets, strongly central sets and v…
-limit points, -cluster points and -Frechet compactness
Manoranjan Singha, Sima Roy
In 2011, the theory of -convergence gets birth as an extension of the concept of -convergence of sequences of real numbers. -limit points…
Force recurrence near zero
Manoranjan Singha, Ujjal Kumar Hom
Considering any dense subsemigroup of the additive semigroup of positive real numbers and a filter associated with it as the domain of thought, various concepts of sets like sets t…
Statistical Compactness
Manoranjan Singha, Ujjal Kumar Hom
Organising the relevant literature and by letting statistical convergence play the main role in the theory of compactness, a variant of compactness called statistical compactness h…
Influence of different kind of thin sets in the theory of convergence
Manoranjan Singha, Ujjal Kumar Hom
A class of subsets designated as very thin subsets of natural numbers has been studied and seen that theory of convergence may be rediscovered if very thin sets are given to play m…
Influence of ideals in compactifications
Manoranjan Singha, Sima Roy
One point compactification is studied in the light of ideal of subsets of . -proper map is introduced and showed that a continuous map can be extended cont…
Compactness with ideals
Manoranjan Singha, Sima Roy
One of the main obstacle to study compactness in topological spaces via ideals was the definition of ideal convergence of subsequences as in the existing literature according to wh…