Hausdorff space
In topology and related branches of mathematics, a Hausdorff space, separated space or T2 space is a topological space in which distinct points have disjoint neighbourhoods. Of the many separation axioms that can be imposed on a topological space, the "Hausdorff condition" (T2) is the most frequently used and discussed. It implies the uniqueness of limits of sequences, nets, and filters.
Hausdorff spaces are named after Felix Hausdorff, one of the founders of topology. Hausdorff's original definition of a topological space (in 1914) included the Hausdorff condition as an axiom.
Definitions
Points x and y in a topological space X can be separated by neighbourhoods if there exists a neighbourhood U of x and a neighbourhood V of y such that U and V are disjoint (U ∩ V = ∅). X is a Hausdorff space if any two distinct points of X can be separated by neighborhoods. This condition is the third separation axiom (after T0 and T1), which is why Hausdorff spaces are also called T2 spaces. The name separated space is also used.
Podcasts:
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by Sick Puppies
Dead Space
by: Sick Puppies[Verse 1]
We have a situation here
It's clear, it's not disappearing
We keep fucking what is pure
No cure, and it keeps happening
Over and over again
Over and over again
We have a situation here
It's clear, it's here
[Chorus]
Dead space
The only thing that's left to fear is
To late to ever start again
They rape us over and over and over and over
But I'm still alive
But I'm still alive in this dead space
[Verse 2]
They're not gonna let us out of here
The fear is taking over
We need to get up out of here
It's clear, the sky is falling
It's falling on top of our heads
It's falling while we're in our beds
They're not gonna let us out of here
They're not gonna let us out of here
[Chorus]
Dead space
The only thing that's left to fear is
To late to ever start again
They rape us over and over and over and over
But I'm still alive
But I'm still alive in this dead space
Dead space
The only thing that's left to fear is
To late to ever start again
They rape us over and over and over and over
But I'm still alive