arXiv subjects

Bedanta Bose

Publications and source records attributed to Bedanta Bose.

5 recordsLinked to original sources

arXiv2024

Zero-Set Intersection Graph On C+(X)

For any Tychonoff space X we have introduced the zero-set in-tersection graph on Γ(C+(X)) and studied the graph properties in connection with the algebraic properties of the semiring C+(X). We have shown that for any two realcompact spaces X and Y the graph isomorphism between Γ(C+(X)) and Γ(C+(Y )), the semiring isomorphism between C+(X) and C+(Y ), the topological homeomorphism between X and Y, the ring isomorphism between C(X) and C(Y ) and the graph isomorphism between Γ(C(X)) and Γ(C(Y )) are equivalent.

math.GN↗

arXiv2021

Abundance of Isomorphic and non isomorphic intermediate rings

It is well known that for a non pseudocompact space X, the family (X) of all intermediate subrings of C(X) which contain bounded real valued continuous functions contains at least 2c many distinct rings. We show that if in addition X is first countable and real compact, then there are at least 2c many rings in (X), no two of which are pairwise isomorphic.

math.GN↗

arXiv2020

D-sets in Arbitrary Semigroup

We define the notion of $D$-set in an arbitrary semigroup, and with some mild restrictions we establish its dynamical and combinatorial characterizations. Assuming a weak form of cancellation in semigroups we have shown that the Cartesian product of finitely many $D$-sets is a $D$-set. A similar partial result has been proved for Cartesian product of infinitely many $D$-sets. Finally, in a commutative semigroup we deduce that $D$-sets (with respect to a Følner net) are $C$-sets.

math.DS↗

arXiv2020

On Cardinality Of Non Isomorphic Intermediate Rings Of C(X)

Let $\sum (X)$ be the collection of subalgebras of $C(X)$ containing $C^{*}(X)$, where $X$ is a Tychonoff space. For any $A(X)\in \sum(X)$ there is associated a subset $\upsilon_{A}(X)$ of $βX$ which is an $A$-analogue of the Hewitt real compactification $\upsilon X$ of $X$. For any $A(X)\in \sum(X)$, let $[A(X)]$ be the class of all $B(X)\in \sum(X)$ such that $\upsilon_{A}(X)=\upsilon_{B}(X)$. We have shown that for first countable non compact real compact space $X$, $[A(X)]$ contains at least $2^{c}$ many different subalgebras no two of which are isomorphic.

math.GN↗

arXiv2016

Discrete $z$-filters and rings of analytic functions

Consider rings of single variable real analytic or complex entire functions, denoted by $\mathbb{K}\langle z\rangle$. We study "discrete $z$-filters" on $\mathbb{K}$ and their connections with the space of maximal ideals of $\mathbb{K}\langle z\rangle$, which we characterize as a compact $T_1$ space $θ\mathbb{K}$ of discrete $z$-ultrafilters on $\mathbb{K}$. We show that $θ\mathbb{K}$ is a bijective continuous image of $β\mathbb{K} \setminus Q(\mathbb{K})$, where $Q(\mathbb{K})$ is the set of far points of $β\mathbb{K}$. $θ\mathbb{K}$ turns out to be the Wallman compactification of the canonically embedded image of $\mathbb{K}$ inside $θ\mathbb{K}$. Using our characterization of $θ\mathbb{K}$, we derive a Gelfand-Kolmogorov characterization of maximal ideals of $\mathbb{K}\langle z\rangle$ and show that the Krull dimension of $\mathbb{K}\langle z\rangle$ is at least $c$. We also establish the existence of a chain of prime $z$-filters on $\mathbb{K}$ consisting of at least $2^c$ many elements.

math.GN↗