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Results tagged with gn.general-topology
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user 81583
Continuum theory, point-set topology, spaces with algebraic structure, foundations, dimension theory, local and global properties.
10
votes
2
answers
426
views
Two questions about the "grasp" cardinal function
For a topology $\mathcal{T}$ on a set $S$, where $\mathcal{T}$ does not have a finite base, I define the grasp $g(\mathcal{T})$ to be the least infinite cardinal $\kappa$ such that $\mathcal{T}$ has a …
- 337
2
votes
1
answer
197
views
If $S$ is non-stationary in $[k]^{\omega}$ is there a choice-function on $S$ with bounded fi...
Fodor's Lemma : When $k$ is a regular uncountable cardinal, and $T$ is a stationary subset of $k$, any regressive $f:T\to k$ has a fiber which is stationary in $k$. Corollary: $T$ is stationary in $ …
- 337
10
votes
1
answer
329
views
Possible cardinalities of the remainders of compactifications of $\Bbb R$
With the usual topology on $\Bbb R$, a compactification $\mathrm{id}_{\Bbb R}:\Bbb R\to v\Bbb R$ can have a remainder $v\Bbb R \setminus \Bbb R$ of cardinality $1,2, 2^{\aleph_0}=\mathfrak c,$ or $2^{ …
- 337