arXiv subjects

C. Ganesa Moorthy

Publications and source records attributed to C. Ganesa Moorthy.

6 recordsLinked to original sources

arXiv2019

Novel Approach to Infinite Products Using Multiplicative Modulus Function

The usual nonnegative modulus function is based on addition. A natural different modulus function on the set of positive reals is introduced. Arguments for results for series through the usual modulus function are transformed to arguments for results for infinite products through the new modular function for multiplication. Counterparts for Riemann rearrangement theorem and some tests for convergence are derived. These counterparts are completely new results and they are different from classical results for infinite products.

math.GM↗

arXiv2019

Lebesgue Spaces and Inclusion Relation

The proofs of A. Villani on inclusion relations among classical Lebesgue spaces are dicussed. The techinque of using closed graph theorem, due to Villani, is applied to derive results on inclusion relations among some more additional spaces. An application of automatic continuity of multiplicative linear functionals on Banach algebras is found.

math.FA↗

arXiv2019

Statistical convergence of nets through directed sets

The concept of statistical convergence based on asymptotic density is introduced in this article through nets. Some possible extensions of classical results for statistical convergence of sequences are obtained in this article, with extensions to nets.

math.GN↗

arXiv2019

Reduction of Quasi-Lattices to Lattices

Quasi-lattices are introduced in terms of 'join' and 'meet' operations. It is observed that quasi-lattices become lattices when these operations are associative and when these operations satisfy 'modularity' conditions. A fundamental theorem of homomorphism proved in this article states that a quasi-lattice can be mapped onto a lattice when some conditions are satisfied.

math.CO↗

arXiv2019

Hausdorffness of General Compactifications

Magill proved that the remainders of two locally compact Hausdorff spaces in their StoneCech compactifications are homeomorphic if and only if the lattices of their Hausdorff compactifications are lattice isomorphic. His construction for compactifications are explicitely discussed through the partitions of their StoneCech compactifications. Partitions in a StoneCech compactification which lead to Hausdorff compactifications are characterized in this article. Embeddings of certain upper semi-lattices of compactifications into lattices of compactifications are constructed.

math.GN↗

arXiv2019

Urysohn Lemmas in Topological Vector Spaces

Two variations of classical Urysohn lemma for subsets of topological vector spaces are obtained in this article. The continuous functions constructed in these lemmas are of quasi-convex type.

math.FA↗