[17215518]

this movie killed me so...I made a playlist

[darypeacher]

[the-overanalyst]

it's always so fascinating and heartbreaking when a character in a story is simultaneously idolized and abused. a chosen prophet destined for martyrdom. a child prodigy forced to grow up too fast. a powerful warrior raised as nothing but a weapon. there's just something so uniquely messed up about singing someone's praises whilst destroying them.

[write-on-world]

[gruntsandpoetry]

lestat next week during the trial trying to simply play his part and not fall down on his knees on the stage and kiss louis' feet and stroke his face and bite him like a cat while calling him mon cher 17 times in a row

[bunnakit]

something something ming's selfishness and unintentionally breaking the mugs with his carelessness

something something joe's selflessness and unable to break the mugs even with intention

idk i'm just saying things recreationally

[mcr-themed-brain]

Alright everybody

[7698]

[unstill-deactivated20260502]

let me stay tender-hearted. despite, despite, despite

katherine mansfield / my stand in, episode six / @headspace-hotel / my stand in, episode six / anaïs nin / my stand in, episode five / (the good place, season two; episode thirteen) / my stand in, episode six

[silversoulsociety]

Giyuu Tomioka

Kimetsu No Yaiba: Hashira Training Arc E1

[smol-ackerman]

SANEMI 🧡

鬼滅の刃 HASHIRA TRAINING ARC: Ep. 03 - Fully Recovered Tanjiro, Joins the Hashira Training!!

[unstill-deactivated20260502]

ming + the first stage of grief: denial

mohammed zarir / @metamorphesque / fortesa latifi / joshua jennifer espinoza / taylor swift

[unstill-deactivated20260502]

joe.

donna tartt, the goldfinch / one direction, a.m. / anne sexton / rebecca solnit, a field guide to getting lost / vampire empire, big thief

[unstill-deactivated20260502]

my stand in, episode four + margaret atwood /david foster wallace / michael cunningham, the hours / emily bronte, wuthering heights / -

[spectracled-eider]

Topological Spaces 10: The Heine Borel Theorem

After out study of product spaces, we now have enough theory to prove the Heine-Borel Theorem is a relatively easy way. There are a couple of things we still need to prove before we can get to the proof.

Whilst we only use one result from the post about product spaces, I still recommend being familiar with it. You can read it here.

First we need two key results that we'll use in our proof.

Proposition 10.1:

Corollary 10.2:

Now we have everything we need to prove Heine-Borel!

Theorem 10.3:

In the next post we will be studying quotient spaces!

[17215518]

this movie killed me so...I made a playlist

[spectracled-eider]

Introduction to Topology Master Post

Metric Spaces

Topological Spaces and Continuity

Closed Sets and Limit Points

Hausdorffness

Connectedness

Path Connectedness

Compactness

Bases and Second Countability

Product Spaces

The Heine-Borel Theorem

Quotient Spaces

Important Examples

Conclusions and Remaining Questions