# New post in General-topology

## Revisit "Prove that the inverse image of an open set is open"

January 17th, 2023

## Why do we need topology and what are examples of real-life applications?

November 3rd, 2022

## the $\sigma$ algeba generated by the class of open intervals with rational end points coincide with the borel $\sigma$ algebra on the real line.

September 29th, 2022

July 30th, 2022

August 1st, 2022

August 1st, 2022

## When is the union of a closed set and a open set open?

February 17th, 2022

## Does a continuous function preserve Hausdorff or metrizable properties?

December 7th, 2020

## ’Stereographic projection’

January 26th, 2020

## Is every point of rational number boundary point?

January 25th, 2020

April 11th, 2020

## Proof that $\mathbb R/[0,1]$ and $\mathbb R$ are homeomorphic

September 10th, 2020

April 12th, 2020

## constant function is continuous

November 17th, 2020

## Continuous function: $Z=${$x \in \mathbb{R} : f(x) = 0$} is closed

November 8th, 2020

August 1st, 2022

## Prove that int$(A) = \overline{[X-A]}$ where $[X - A]$ is the closure and the bar represents the complement.

August 16th, 2020

May 10th, 2020

## show a set is connected

February 23rd, 2020

May 30th, 2020

## Compact Connected Set in $R^2$ and Connected Component

September 6th, 2020

August 1st, 2022

March 17th, 2020

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

## Example of discrete set

February 3rd, 2020