# All Questions

98,519 questions
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### Name for mappings that are “not quite projections”

Is there a known name for the following definition? Consider topological spaces $X$, $Y$ and $f: X \rightarrow Y$ a continuous mapping. Then, $f$ is an "almost projection" if there is a topological ...
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### Uniqueness of limits and compactness implies closure

It is not difficult to prove that in a Hausdorff topological space every compact set is closed, and almost trivial that if in a topological space X every compact set is closed then X is T1. As ...
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### Specific examples of an algebraic closure of a finite field [on hold]

I'm struggling to understand the concept of algebraic closure for finite fields. Are there specific examples I can use to get an intuitive understanding? What sorts of elements do the algebraic ...
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### Theory of surfaces in $\mathbb{R}^3$ as level sets

Is there a book that treats the classical theory of surfaces in $\mathbb{R}^3$ from the point of view of level sets of a function? I seem to remember someone telling me that such a book exists, but I ...
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### $m-$cycles in $S_n$ modulo an equivalence relation

Let $A$ be the set of all $m-$cycles in $S_n$. Define an equivalence relation $i$ in $A$ by $\sigma_1$ is related to $\sigma_2$ by $i$ if $\sigma_1$ is a power of $\sigma_2$ or viz., then the number ...
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### Intersection of $\{2^a 3^b 5^c 7^d\}$ and its translates
Let $S$ be the set of positive integers of the form $2^a3^b 5^c 7^d$. I need information about the cardinality of the intersection of $S$ and its translates. In particular, is $S \cap (S+t)$ ...
### A computing shortcut to $Dedekind Number(n)$?
OEIS A132581 gives a functional extension of Dedekind numbers. $F(n)$ is the number of antichains in the first $n$ elements of "the infinite boolean lattice". And \$\operatorname{DedekindNumber}(e) =...