Title- Completeness of finite and infinite dimensional Normed Linear Spaces
Speaker- Mukesh Mithun A D (BSMS 23)
Date- October 29, 2024(Tomorrow)
Time- 9 pm
Venue- will be informed
Abstract: Vector spaces are a set of elements following a certain structure, when a norm is defined for a vector space we make it a Normed Linear Space. Since it’s a metric space now we can talk about the topology induced on the vector space by the norm, one of the very nice properties to look out for is that the vector space under a norm is whether it is complete or not, when we go searching about these spaces we realize that the completeness of the space isn’t dependent on the choice of vector space for the countable dimensions. The talk is about how all normed finite dimensional spaces are complete and all normed infinite dimensional spaces are incomplete and how the case of uncountable infinite dimensions differ in the sense of completeness.