The above is the letter presenting the resignation of the editorial board of Topology, an Elsevier journal. The journal has been discontinued as of this year.

[…] As you are well aware, the Editors have been concerned about the price of Topology since Elsevier gained control of the journal in 1994. […] The journal Topology has an illustrious history with which we, on becoming editors, were extremely proud to be associated. […] However, we feel that Elsevier’s policies towards the publication of mathematics research have undermined this legacy.

Therefore, with great reluctance and sadness, we have made the difficult decision to resign. […]

On Google+, David Roberts gave a link to the journal’s site, with some highlights: As you can see here, the last published issue (vol. 48, 2-4) was June-December 2009. The previous issue was 40 pages and consisted of 2 papers (that you can purchase access to, at $31.50 each. Plus tax.) And there is also a supplement, published on December 2011. Only $31.50 (plus tax) for a 4 page correction.

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I am looking for references discussing two inequalities that come up in the study of the dynamics of Newton's method on real-valued polynomials (in one variable). The inequalities are fairly different, but it seems to make sense to ask about both of them in the same post. Most of the details below are fairly elementary, they are mostly included for comp […]

Let $C$ be the standard Cantor middle-third set. As a consequence of the Baire category theorem, there are numbers $r$ such that $C+r$ consists solely of irrational numbers, see here. What would be an explicit example of a number $r$ with this property? Short of an explicit example, are there any references addressing this question? A natural approach would […]

Not necessarily. That $\mathfrak m$ is consistently singular is proved in MR0947850 (89m:03045) Kunen, Kenneth. Where $\mathsf{MA}$ first fails. J. Symbolic Logic 53(2), (1988), 429–433. There, Ken shows that $\mathfrak{m}$ can be singular of cofinality $\omega_1$. (Both links above are behind paywalls.)

Ignas: It is not possible to provide an explicit expression for a non-linear solution. The reason is that (it is a folklore result that) an additive $f:{\mathbb R}\to{\mathbb R}$ is linear iff it is measurable. (This result can be found in a variety of places, it is a standard exercise in measure theory books. As of this writing, there is a short proof here. […]

MR2449474 (2009j:03067) Woodin, W. Hugh. A tt version of the Posner-Robinson theorem. Computational prospects of infinity. Part II. Presented talks, 355–392, Lect. Notes Ser. Inst. Math. Sci. Natl. Univ. Singap., 15, World Sci. Publ., Hackensack, NJ, 2008. The proof is nice, invoking both recursion-theoretic and set-theoretic tools. Hugh uses a Prikry-like f […]

There is a general argument without choice: Suppose ${\mathfrak m}+{\mathfrak m}={\mathfrak m}$, and ${\mathfrak m}+{\mathfrak n}=2^{\mathfrak m}$. Then ${\mathfrak n}=2^{\mathfrak m}.\,$ This gives the result. The argument is part of a nice result of Specker showing that if CH holds for both a cardinal ${\mathfrak m}$ and its power set $2^{\mathfrak m}$, th […]

By Fermat's little theorem, $t^p\equiv t\pmod p$ for any $t$, so if $p\mid x^p+y^p$ then in fact $p\mid x+y$ (or $y\equiv -x\pmod p$). Now, since $p$ is odd, $$x^p+y^p=(x+y)(x^{p-1}-x^{p-2}y+x^{p-3}y^2-\cdots+y^{p-1}).$$ The first term is a multiple of $p$, as explained above. The second is $$\sum_{k=0}^{p-1}(-1)^k x^{p-1-k}y^k=\sum_{k=0}^{p-1}x^{p-1-k} […]

Your idea is sound, but it requires more work. As pointed out, you have only described so far a very small subcollection of the Borel sets. Instead, show that you can associate to each Borel set a code that keeps track of the "history" of its construction starting from basic open sets, and then count the number of such codes. There is a lot of leew […]

Recently, I was reading Hardy's Orders of Infinity (available here or here): Godfrey Harold Hardy. Orders of infinity. The Infinitärcalcül of Paul du Bois-Reymond. Reprint of the 1910 edition. Cambridge Tracts in Mathematics and Mathematical Physics, No. 12. Hafner Publishing Co., New York, 1971. MR0349922 (50 #2415). The book discusses this result, so […]

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