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Results tagged with gn.general-topology
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user 37728
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
-2
votes
1
answer
386
views
non-trivial convergent sequence [duplicate]
I have reached a deadlock to find a example to show that a compact Hausdorff space does not need to have a no non-trivial convergent sequence.(except $\beta\omega$)
can you give me a example of …
- 147
-1
votes
1
answer
669
views
Stone-Cech compatification and ultrafilter [closed]
I have been studding about compatification of a topological space $X$. But I have low understanding about the Stone-Cech compatification, specially construction of the Stone-Cech compatification on na …
- 147
11
votes
4
answers
2k
views
Non-trivial convergent sequence in Stone-Čech compactification of $\mathbb{N}$
Why are there only trivial convergent sequences in the Stone-Čech compactification of $\mathbb{N}$?
- 147
1
vote
1
answer
577
views
T2 ⇒ KC ⇒ US ⇒ T1
In a topological KC-space, every compact space is closed.
In a US-space, each convergent sequence has a unique limit.
So, T2 ⇒ KC ⇒ US ⇒ T1, but the converse implications do not hold.
(a): Can yo …
- 147