How the continuum hypothesis is related to the solution of a question in complex analysis [Prof. Shameek Paul, RKMVERI]

Post published:December 11, 2023
Post category:News & Events

INVITATION

Co-Curricular: How the continuum hypothesis is related to the solution of a question in complex analysis [Prof. Shameek Paul, RKMVERI]

Type: Co-Curricular – Other

Event Date: 07 Dec 2023

Venue: Math Dept

Campus: Belur Campus

Department: Mathematics

Dear all,

This is a gentle reminder to the next colloquium talk. Tomorrow, on 7th December at 5pm, Prof. Shameek Paul will talk about

"How the continuum hypothesis is related to the solution of a question in complex analysis".

As usual, the talk will take place in class room 402.

The following talk will be by Prof. Sagnik Chakraborty on Wednesday, 13th December at 5pm. An abstract and title will be given soon. Below is the abstract for tomorrow's talk by Prof. Shameek Paul.

Best wishes,

Stephan

Abstract: The continuum hypothesis states that every uncountable subset of $\mathbb{R}$ is in bijection with $\mathbb{R}$ . The following question was asked by Wetzel and its surprising answer was provided by Paul Erdos. https://en.wikipedia.org/wiki/Wetzel%27s_problem If $\mathcal S$ is a set of entire functions such that for every $z\in \mathbb{C}$ the set $\{f(z):f\in\mathcal S\}$ is countable, then can we say that $\mathcal S$ is countable? Although the converse of this statement is easily seen to be true, the answer to this question depends on the continuum hypothesis. We will assume the result that if the continuum hypothesis holds, then there exists a well-ordering on $\mathbb{C}$ such that for every $a\in \mathbb{C}$ the set $\{z\in \mathbb{C}:z<a\}$ is countable.