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14h

comment 
In set theory, is there a name for a function which maps the empty set to zero and all the others to one?
$0^{0^S}$  wonderfully concise and intransparent. 
19h

revised 
Continuous image relation on topological spaces
nonHausdorff is the main point, not "finite". 
1d

comment 
Freiling's Axiom of Symmetry Concretized
To prove "my" version from "your" version, just apply "your" version to the function $g(x):= f(x) \setminus \{x\}$. 
1d

comment 
Freiling's Axiom of Symmetry Concretized
If you demand that $x\notin f(x)$ for all $x$, then the free set $F$ will have the property $y\notin f(z)$ for all $y,z\in F$. If you do not demand this, you get $y\notin f(z)$ only for all distinct $y,z\in F$. 
2d

answered  Freiling's Axiom of Symmetry Concretized 
2d

answered  Continuous image relation on topological spaces 
2d

comment 
Continuous image relation on topological spaces
I am not sure if the empty set is considered a topological space, but in the context of this question it certainly should not be. 
Mar 24 
reviewed  Close Probability or odds of something happening 
Mar 24 
awarded  Nice Answer 
Mar 24 
answered  Connectedness in the language of pathconnectedness 
Mar 24 
comment 
Connectedness in the language of pathconnectedness
Very long lines exist. Let $\kappa$ be any cardinal (viewed as an ordinal). For each $\beta$ in $\kappa$ add a copy of the unit interval between $\beta$ and $\beta+1$, plus a point $\infty$. The resulting linear order is dense and complete. But if $C$ has cardinality smaller than $\kappa$, then any continuous image of $C$ that contains $0$ and $\infty$ will not be onto, hence not connected. 
Mar 24 
comment 
The product of the power and the natural number in the short interval
I do not understand the role of $a$ and $n$ here. Can't you just write $A$ for $a^n$? 
Mar 24 
comment 
Mal'cev “rational equivalence” and model theory
Concerning the modeltheoretical point of view: The two structures use different languages, so formally the formulas satisfied in one structure are not the same as those satisfied in the other. But the assumption of "rational equivalence" implies that there are natural translations in both directions. 
Mar 24 
comment 
Mal'cev “rational equivalence” and model theory
Contrariwise. "rational equivalence" of two algebras implies that their clones are isomorphic. It is the other direction that is not necessarily true. 
Mar 23 
answered  Mal'cev “rational equivalence” and model theory 
Mar 23 
comment 
Is $\mathcal{P}(\omega)/fin$ with the interval topology a connected space?
Nice! In SteenSeebach's "Counterexamples in topology" such spaces where any two nonempty open sets intersect are called hyperconnected. 
Mar 23 
comment 
Antichain on $\mathcal{P}(\omega)/fin$ of cardinality $2^{\aleph_0}$?
Related question: mathoverflow.net/questions/89306/… 
Mar 23 
reviewed  Approve hilbertspaces tag wiki excerpt 
Mar 17 
answered  On surjections, idempotence and axiom of choice 
Mar 17 
comment 
Surjective marriages
Yes iff $M$ is finite. 