In this article, in a generalized metric space, we will focus on new types of sequences. We intro... more In this article, in a generalized metric space, we will focus on new types of sequences. We introduce three new kinds of Cauchy sequences and study their significance in generalized metric spaces. Also, we give several interesting properties of these sequences.
We introduce two types of strongly nowhere dense sets, namely (s, v)-strongly nowhere dense set, ... more We introduce two types of strongly nowhere dense sets, namely (s, v)-strongly nowhere dense set, (s, v)*-strongly nowhere dense set and analyze their characteristics in a bigeneralized topological space (BGTS). Further, it is also given some relations between these two types of strongly nowhere dense sets along with its various properties for (s, v)*-strongly nowhere dense set. Finally, the necessary and sufficient condition is found between \mu-strongly nowhere dense set and (s, v)*-strongly nowhere dense set in a BGTS.
We consider the unital Banach algebra $\ell ^{1}(\mathbb{Z}_{+})$ and prove directly, without usi... more We consider the unital Banach algebra $\ell ^{1}(\mathbb{Z}_{+})$ and prove directly, without using cyclic cohomology, that the simplicial cohomology groups ${\mathcal{H}}^{n}(\ell ^{1}(\mathbb{Z}_{+}),\ell ^{1}(\mathbb{Z}_{+})^{\ast })$ vanish for all $n\geqslant 2$. This proceeds via the introduction of an explicit bounded linear operator which produces a contracting homotopy for $n\geqslant 2$. This construction is generalised to unital Banach algebras $\ell ^{1}({\mathcal{S}})$, where ${\mathcal{S}}={\mathcal{G}}\cap \mathbb{R}_{+}$ and ${\mathcal{G}}$ is a subgroup of $\mathbb{R}_{+}$.
In this article, in a generalized metric space, we will focus on new types of sequences. We intro... more In this article, in a generalized metric space, we will focus on new types of sequences. We introduce three new kinds of Cauchy sequences and study their significance in generalized metric spaces. Also, we give several interesting properties of these sequences.
We introduce two types of strongly nowhere dense sets, namely (s, v)-strongly nowhere dense set, ... more We introduce two types of strongly nowhere dense sets, namely (s, v)-strongly nowhere dense set, (s, v)*-strongly nowhere dense set and analyze their characteristics in a bigeneralized topological space (BGTS). Further, it is also given some relations between these two types of strongly nowhere dense sets along with its various properties for (s, v)*-strongly nowhere dense set. Finally, the necessary and sufficient condition is found between \mu-strongly nowhere dense set and (s, v)*-strongly nowhere dense set in a BGTS.
We consider the unital Banach algebra $\ell ^{1}(\mathbb{Z}_{+})$ and prove directly, without usi... more We consider the unital Banach algebra $\ell ^{1}(\mathbb{Z}_{+})$ and prove directly, without using cyclic cohomology, that the simplicial cohomology groups ${\mathcal{H}}^{n}(\ell ^{1}(\mathbb{Z}_{+}),\ell ^{1}(\mathbb{Z}_{+})^{\ast })$ vanish for all $n\geqslant 2$. This proceeds via the introduction of an explicit bounded linear operator which produces a contracting homotopy for $n\geqslant 2$. This construction is generalised to unital Banach algebras $\ell ^{1}({\mathcal{S}})$, where ${\mathcal{S}}={\mathcal{G}}\cap \mathbb{R}_{+}$ and ${\mathcal{G}}$ is a subgroup of $\mathbb{R}_{+}$.
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Papers by Yasser Farhat