abstract algebra: why is the canonical projection map from a topological group to a quotient space an open map?

Leave $ G $ be a topological group and $ H $ A closed subgroup. Define $ pi: G a G / H $ by $ g mapsto gH $ and equip $ G / H $ with the topology induced by $ pi $, that is, the best topology such that $ pi $ It is continuous A text that I am reading affirms that it is "clear" that $ pi $ It is an open map, that is, for each open $ V in G $ we have that $ pi (V) $ It's open.

This is not clear to me at all.

A necessary and sufficient condition for $ pi (V) $ be open in $ G / H $ is for the whole

$$ bigcup_ {v in V} vH $$

be open in $ G $. I don't know how I can say anything like this since this may be a larger set than $ V $, and who knows which sets are or are not in the topology of $ G $.

I suspect that I'm missing something very obvious?

obfuscation: industry safe file format like .OFX Open Financial Exchange File

The .OFX Open Financial Exchange file is a file format created for financial data exchanges between financial institutions.

I was wondering if there is such a file format in the IT security arena.

My goal would be to use and customize it for my backend API entry points (that's another story, don't worry about that)

tar – How can encrypted Apple DMGs open so fast?

On the remote disk I have an encrypted .dmg and the same files in a gpg encrypted tar file.
The DMG opens in seconds, but to access the tar file, I first need to decrypt it, in these 10 minutes, and then expand it, another 10 minutes.

How can Apple DMG be so fast? or where do I read more about how it works?

What open source project management systems accept a Teamwork.com data export import?

I have some old data on Teamwork.com that I would like to keep for history / posterity, but couldn't find any option to import the exported database to another free / open source service. Any option that I may be missing in this regard?

18.04 – Unable to SSH but need to open ubuntu terminal to fix it

I was setting up my apache server on ubuntu 18.04, while checking the firewall, I used some commands like sudo ufw allow enable and did not enable ssh, my SSH post is not working. Now I can't access the server through putty using port 22.

I need to run sudo ufw allow ssh to enable 22, but how do I enter this command while ssh doesn't work and I don't have access to my server terminal?

Why does the scan result sometimes open and sometimes leak or close?

My colleague told me it was blocked from the telecom side, the first nmap scan is leaked, but then I run it again, it comes back open

Then I use what is my IP address.com to scan, first the scan closes, then I run the scan again, reopen

investigation – List of open problems in Number Geometry?

The first time I encountered Geometry of Numbers in Hardy's book Introduction to Theory of Numbers I was very interested in the subject. I studied Number Geometry by C D Old, then I'm in the middle of a much more difficult Cassels book

I want to write my bachelor thesis on the list of famous open problems in number geometry and explain each one. But unfortunately there is no list available on the Internet! (except for a problem related to Diophantine's approximation, Littlewood's conjecture) Please help! Thank you.

windows – How to open files in the same Mathica instance?

I just installed version 12.1 and a new default setting is bothering me. Previously, when you used to open a notebook and after opening another, it used to open in the same instance of Wolfram Desktop instead of creating a new one every time. Is there an option to change this behavior again?

[ Politics ] Open question: is it illogical to blame Trump for the corona virus?

[Politics] Open-ended question: Is it illogical to blame Trump for the crown virus?

[ Politics ] Open question: The Chinese virus is exaggerated, is this an attempt at distraction while something else is being done?

Lolly, more like a baby died from X, but since it turned out positive for Ching Chong, that's what killed him. You are another stupid woman. LOL Humpty the sunscreen, I don't even know anyone who is ill NM died. I know a guy who does a show on JudenTube who says he knows a guy who has it. Hahaha 4.7% mortality rate mi ***. We will not even reach 100k at this rate, deaths today were lower than yesterday. Hahaha I don't want to be in New York surrounded by a bunch of dirty non-whites.