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Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.

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 …
maryam's user avatar
  • 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 $\mathbb{N}$?
maryam's user avatar
  • 147
-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 …
maryam's user avatar
  • 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 …
maryam's user avatar
  • 147