Hausdorff moment problem Puns

I've come across this rather convoluted problem:

Let X be a topological space, Y a hausdorff space, and f: X -> Y continuous. Let C be a closed subset of Y, and U an open subset of X such that U contains f-1(C). If X is compact, there exists an open neighborhood V containing C such that f-1(V) is contained within U.

The question now is: Find an example where X is not compact and such neighborhood V doesn't exist.

The fact that Y is Hausdorff prevents me from using the standard pathological counterexamples with discrete and trivial topologies. I assume that Y will then be some subset of the real numbers. X is not compact, so I've tried with different open and semi-open intervals for X, but nothing seems to work.

I've tried the standard pathological functions, Thomae's function, Dirichlet's function.. I'm really not sure what to do here. Any guidance would be tremendously helpful.

Listen up. The following is the brainchild of an individual called NK, we met in a Level 2 Data Youtube stream. I am posting on their behalf. ____________________________________________________________________________________________________________

Hi r/Superstonk,

Today I am bringing a theory I would like all of you to pick apart and give your thoughts on. I have read some fantastic DD over the past year and after u/yelyah2’s post today it just… clicked. I am not bringing data, this is an explanation for the events we are seeing.

Before I present the theory, I just want to state some assumptions I am making based on available information.

1. In the years before 2020 GameStop was not doing well and COVID19 did not help. A lot of shorters saw an opportunity and went all-in.
2. I believe there is a separation between ‘shorters’ (hedge funds, family offices, banks… ) and market makers. They may be colluding, but there does not seem to be enough evidence for it.
3. However many times the float might be owned by retail, it does not matter, the events playing out signify the amount is enough.
4. There are a lot of tinfoil theories. I am ignoring them to base this theory on known, simple facts.
5. I cannot provide a timeline.
6. Although I have an economic background, this is not financial advice.

Buckle up.

Over the last weeks we have seen a lot of activities play out, including the dramatic price rise and drop over the last weeks. In my opinion, these activities are and may always have been market makers preparing to bring the necessary liquidity to the market, not necessarily to shake out retail.

Between April and August of 2020, Ryan Cohen bought a 9% (5.8 million shares) in GameStop. He upped this number to 13.9% into November 2020. I believe Mr. Cohens purchase of shares combined with the retail investors following him by buying shares and options, was enough to bring the market – the supply of GME stock - to the point of illiquidity. At the start of December, a huge delta spike was triggered during a similar price decrease as this year. As you could read in u/yelyah2’s post, it means the option market thinks the underlying (stock) is

I'm trying to get better at setting boundaries. Not all of these problems are huge things. I also don't like the idea of just bringing it up as it's happening because a. I really struggle to put my thoughts in order enough to verbalize them and b. I don't want to lash out at the peak of being frustrated or dysregulated. Id rather take some time and calm down, and then bring up the issue later without causing harm to the other person.

I never ever freaking remember to bring it up. I just jump from one thing to another like always. Im realizing how much this has impacted my friendships too, especially close ones, because I never seem to be able to get around to talking about something or discussing compromises. I just freak out in the moment and move onto the next thing without meaning too and it is so frustrating.

Does anyone else struggle with this? Any suggestions? Im thinking about writing notes to myself if I can and then going them over later when I feel calmer, but sometimes I forget to check notes as well unless they are right in front of me.

Anyone who's ever flown in SC or ED knows that shutting down your engines while traveling doesn't bring you to a halt. Your ship just continues on its way, if you are planet side gravity will drag you to the ground post haste. But in the black - you just continue on your current vector until you hit something or explode.

Thats a problem for piracy. Right now in both ED and SC, disabling a running ship just means that you are now chasing a powerless hulk. There are creative ways to stop it. In Elite you can use cannons to slow it, but you risk blowing up the ship and the booty with it. In both games, getting ahead of the ship, gently making contact with it and slowing it down is the main way to do this.

This is unacceptable especially in SC where touching two ships together is spinning the roulette wheel on what crazy outcomes an engine under construction wants to dish out. We have tractor beams, but its already been said ship grabbing with tractor beams is risky business. Has any mention of a solution to this been given?

I know there will be many of you who say "its piracy its supposed to be hard." and you'd be correct - it IS hard, but this element transcends gameplay. You can do everything right as a pirate up to this point and have it all completely undone not by any doing of the player you're pirating, not by a mistake you made, but by the lack of tools for this type of gameplay to make sense. Thats not okay.

I tried proving this using induction, then when I looked up the proof on Google to see whether I'd missed the mark or not, a lot of the people who proved this just used contradiction or contrapositive. I wondered if my proof with induction was still valid, even if it is less simple and elegant than the contradiction proof.

Proof:

Let N_1 be a neighborhood of p. Then since p is a limit point, N_1 contains some p_1 ∈ A such that p_1 ≠ p. Further, because X is Hausdorff, there's some Z_1 of p_1 and Y_1 of p such that Z_1 ∩ Y_1 = {}. Set N_2 = Y_1 ∩ N_1. Since both Y_1 and N_1 are neighborhoods of p, then N_2 is open and contains p and thus is also a neighborhood of p, which, in particular, does not contain p_1.

Proceeding via induction, we shall assume that for all i ≥ 2, N_i = N_(i-1) ∩ Y_(i-1) is a neighborhood of p that doesn't contain p_(i-1). Clearly then, N_i contains no p_k for k ≤ i -1. Since N_i is a neighborhood of p, it contains some p_i ∈ A such that p_i ≠ p. Also, since X is Hausdorff, there's a neighborhood Z_i of p_i and Y_i of p such that Z_i ∩ Y_i = {}. Because Y_i doesn't contain p_i, then N_i ∩ Y_i is a neighborhood of p that contains no p_k for k ≤ i.

Based on this, it is clear that each N_i is a subset of N_(i-1), and so N_1 contains every N_i for i ≥ 1. Because each N_i contains a unique p_i ∈ A such that p_i ≠ p and p_i ≠ p_k for k ≤ i -1, then there are at least as many points of A in N1 as there are natural numbers, I.E., N_1 contains an infinite amount of points of A. △

What are your thoughts on this? Is it valid or do I kind of have to do this proof using contradiction? As a side note, if you have suggestions on improving my proof writing I am wide open. I tried to make this as readable as I can on Reddit. Thanks for your time!

Source: https://theathletic.com/2885135/2021/10/12/amick-kyrie-irving-proves-again-hes-comfortable-being-uncomfortable/

> One thing is for sure — at least for now. While an Irving trade for Ben Simmons with Philadelphia is seen by some as an easy solution to both teams’ problems, sources with knowledge of the 76ers’ view said there is no interest in Irving at the moment. From management on down, it seems there is an unsurprising level of skepticism about that pairing working out any better than the Joel Embiid-Simmons duo that is zombified at the moment.

> And in the absence of Irving getting an extension from the Nets — which is obviously not happening now — the other tricky part here is that he can opt out of his deal after this season. That’s obviously a major factor for any interested team.

I’ve been making this video series with my parents (both of whom are therapists) about different mental fitness strategies, this week's video covers 3 effective grounding techniques to reduce anxiety.

Hope you find it helpful :)

https://youtu.be/6AhPCglzWEc

Can someone please explain the difference between a Hausdorff space and a disconnected space?

If each of the main six were represented as a topological space with the property that any two points belong to disjoint open sets, then who would get what? Bonus points for proofs that the spaces are Hausdorff.

Realized a little bit ago I may have a problem with how much Nightwish gear I own. It wasn't intentional really with what I'm wearing. It's Friday and I work from home. I wear t-shirts on Fridays. So I grabbed a Nightwish one because it was the first one I saw.

Then I like to wear necklaces. So I put on my current favorite necklace....the silver ammonite from Nightwish. I bought it as a reward for a promotion and new job.

And where my home office is by two walls of windows. It's breezy and cold. So I grab the Human Nature ruana/cape to stay snuggly warm in.

I thought if anyone is this world could appreciate this and laugh with me, it would be you all.

Anyone else have a moment of "you know you're a fan when..."?

This as the removal of the dogs is impossible right now

Not sure if this is the right subreddit but I'm teaching myself topology right now and was reading about Hausdorff spaces when I clicked on Felix Hausdorff's wiki page on a whim. Apparently he was persecuted by the Nazis for his background. Things got worse after Kristallnacht and he ultimately ended up committing suicide with his wife and sister-in-law when they were ordered to relocate. I did not expect one of the main founders of the math topic I'm learning right now to have been a victim of the Holocaust... Terrible.

I have 4 finite sets (A, B, C, D). Each set contains 5000 vector points with a dimension of 100.

All vector points have normalized length to 1. And A, B, C, D are mean centered. It means that the average vector is Zero vector.

I was trying to measure the Hausdorff distance between the each 2 pair sets (A-B , A-C, A-D, B-C ...).

these are the results of some experiments:

Experiment for A-B 
Hausdorff Manhattan distance test: 21.326246978327426
Hausdorff euclidean distance test: 1.3508576679570408 
Hausdorff Chebyshev distance test: 0.18304568600782653 
Hausdorff cosine distance test: 0.8957927799096113   

Experiment for A-C 
Hausdorff Manhattan distance test: 21.235883122208914 
Hausdorff euclidean distance test: 1.3518369761317137 
Hausdorff Chebyshev distance test: 0.18463063544698438 
Hausdorff cosine distance test: 0.8825133826676205   

Experiment for A-D 
Hausdorff Manhattan distance test: 20.661629390233674 
Hausdorff euclidean distance test: 1.3039618701736158 
Hausdorff Chebyshev distance test: 0.18129206130133735 
Hausdorff cosine distance test: 0.8355905657774667   

Experiment for D-C 
Hausdorff Manhattan distance test: 21.395568267647146 
Hausdorff euclidean distance test: 1.350181456390644 
Hausdorff Chebyshev distance test: 0.18708208775037113 
Hausdorff cosine distance test: 0.8852382719181378  

Experiment for B-C 
Hausdorff Manhattan distance test: 21.34285872204752 
Hausdorff euclidean distance test: 1.3497651948873144 
Hausdorff Chebyshev distance test: 0.18461430734152376 
Hausdorff cosine distance test: 0.8796709556949005 

Why all the results for all pairs are too close? Knowing that the sets are totally independent?

Hi,

How Scaling Exponent, Holder Exponent And Hausdorff dimensions are related? With what logic (Mathematical and intuitive) we can navigate between these concepts.

I wanted to watch some Oregairu today but got a warning for malware-website when trying to click on the videos. It’s a legitimate warning. I use my iOS device to stream it via AirPlay on my TV.

The report says this

The ntebfvnpmf.xyz website contains malicious content, including pages that Redirect visitors to malicious websites Trying to trick visitors into sharing personal information or downloading software.

But when entering the website the domain still remains GogoanimeDOTcm

It worked all fine yesterday, considering the website is saved as an app icon on my mobile device. I also use an AdBlocker for my phone that surprisingly works, I don’t know if this information is viable to you guys. Also the ads get blocked but usually I get redirected to other websites before using Gogo where I can totally identify fake virus warnings. But like I said, this one is legitimate.

Whenever we boot up valorant we expect the setting to be the same and not randomized each time, but this is an issue in the Video stats section and it really bugs me a lot, here are some pic's of the first boot and the second boot

First boot

Second boot

I don't know the reason it does this but it has been doing this since the latest patch but lets hopefully find a fix to this

In previous Halo titles that allowed armor customization you used to see someone with a unique armor piece and think to yourself “oh wow, this guy unlocked that by doing A, B, and C. That’s cool.” But now with the way armor and cores and colors all work what I’ve noticed is anytime I see someone who looks overly different I don’t think it’s cool. All I can think is “oh look at this dickhead who spent a bunch of money already in the store to get some different armor.”

That’s a pretty big issue if you ask me when 343 stated that they wanted all the Spartans to look unique.