Mathematics
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Sourav Ghosh
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About

A Graduate student of mathematics.

Some of my questions, I am still searching for better answers....

Favorite ) A sort of converse of Banach-Steinhaus theorem.

  1. Can we define any metric on $\Bbb{R^\omega}$ so that it represents a norm?

  2. Does there exists any non trivial linear metric space in which every open ball is not convex?

  3. Why not we avoid the phrase "if we assume AC " and take it as granted?

  4. What are the minimum conditions for an open ball in $(X, d) $, $X$ is a linear space to be convex?

  5. Can you give me an example of a non compact topological space with compact dense subset?

  6. How to construct a real valued function which is continuous only on a given $G_\delta$ subset of $\mathbb{R}$?

  7. Is there any condition that makes a measure zero set countable?

  8. ${\scr{B}}(A, Y) \cong {\scr{B} }(X, Y) $ (isometically Isomorphic)

  9. Can we classify all topological space $(X, \tau) $ where every second category sets are Residual sets?

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View all questions and answers
All Questions Answers
Score Newest
question
10
Can we define any metric on $\Bbb{R^\omega}$ so that it represents a norm?
Dec 15, 2021
question
7
Does there exists any non trivial linear metric space in which every open ball is not convex?
Dec 15, 2021
question
6
Given $G=\langle a\rangle$, $|G|=n$ and $d\mid n$, show $G$ has a unique subgroup of order $d$.
Dec 10, 2021
question
5
Can you give me an example of a non compact topological space with compact dense subset?
Nov 24, 2021
question
5
Why not we avoid the phrase "if we assume AC " and take it as granted?
Dec 14, 2021
answer
5
Continuity of function - Proof verification
Dec 13, 2021
answer
5
If $G$ is a group and $|G|=6$ show that there exists a $a \in G$ such that $O(a)=6$
Apr 28
answer
4
What is a path in a topological space?
Apr 27
answer
4
Find all continuous function from $(\mathbb{R},d_{2})$ to $(\mathbb{R},d_{disc})$ and all continuous function other way around
Jan 1
question
4
Why was the concept of first/second categories in metric spaces introduced?
Jan 20

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