Ramiro de la Vega
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Registered User
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1d |
answered | Do operations generate well-ordered sets only? |
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2d |
answered | Importance of separability vs. second-countability |
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May 18 |
accepted | Is there a contractible bounded homogeneous space? |
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May 17 |
answered | Is there a contractible bounded homogeneous space? |
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May 15 |
answered | How far is Lindelöf from compactness? |
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May 10 |
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Does this property of a partially ordered set have a name? @Goldstern: Thats's right, my comment about well-met posets was answering a question made by Butch in another comment not the original question. Sorry for the confusion. |
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May 9 |
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Does this property of a partially ordered set have a name? That´s sometimes called a well-joined (well-met for the dual notion) partial order. |
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May 9 |
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Does this property of a partially ordered set have a name? Trees also have this property. |
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May 6 |
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Which topological spaces are coset spaces of locally compact groups? Condition 3) is not necessary unless you restrict to compact G´s. |
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Apr 25 |
awarded | ● Nice Answer |
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Apr 25 |
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Maximal chains in vector space and its dimension Typically a subset of a partially ordered set is a chain if any two elements are comparable (i.e. it is linearly ordered). Inside any chain you can always find a cofinal well-ordered chain, but that´s another story. |
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Apr 17 |
answered | Regular spaces that are not completely regular |
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Apr 12 |
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Closed totally disconnected subspaces Mathieu, could you please say a word or two about why your space is locally compact Hausdorff (so that it has a one-point compactification) and why a closed set in the compactification containing the "infinite" point cannot be totally disconnected and of size $\omega_{\omega_1}$? |
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Apr 11 |
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Does there exist a topology for a set X which is compact and Hausdorff? Or one point compactifications of discrete spaces, in case you want to avoid the axiom of choice. |
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Apr 9 |
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Is there a “mathematical” definition of “simplify”? I always thought the preference of $\frac{\sqrt{2}}{2}$ over $\frac{1}{\sqrt{2}}$ comes from the pre-calculators era. To compute the former you look for $\sqrt{2}$ in a table an then divide by $2$ by hand. To compute the latter you first need to "rationalize" the expression as you learned in your remedial math course. |
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Apr 8 |
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Countable coloring of a plane Jakub, it would be good if you explained a little bit where the problem came from and why you think such decomposition should exist. |
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Apr 3 |
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How to work out a grammar if we know the language? I´m not sure what you mean by algorithm here, since there are uncountably many possible inputs (languages). |
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Apr 2 |
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Is the image of discrete set under an open map discrete? Can´t you just add an extra $\mathbb{Z}$ factor to $G$ and $H$ and then let $Y$ be generated by the element $(1,0,1,1,1,\dots)$? |
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Mar 20 |
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Which topological spaces are (topological) groups? Made a statement more precise |
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Mar 20 |
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How to prove a quadratic equation has at most two roots in first order theory of field @John L: In the event that your question doesn´t get closed, you still need to specify what your deductive system is, before getting any kind of real answer. First order logic has many different complete deductive systems and formal proofs for the same sentence may look very different in different systems. |
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Mar 20 |
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How to prove a quadratic equation has at most two roots in first order theory of field This first order theory is not complete (e.g. it cannot prove or disprove that 1+1=0). Still it is true that a sentence that is true in every field must have a proof (this is completeness of first order logic not completeness of the theory of fields). In any case I don´t think this question is appropiate for MO since it is a standard exercise in a basic logic course. |
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Mar 19 |
revised |
Put positive polynomial in finite intersection of half-spaces Fixed latex |
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Mar 19 |
accepted | Can we generalize the result of Urysohn’s lemma to countable collection of pairwise disjoint closed subsets of a normal space..? |
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Mar 18 |
answered | Can we generalize the result of Urysohn’s lemma to countable collection of pairwise disjoint closed subsets of a normal space..? |
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Mar 11 |
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Reference needed: Does pseudo laminated compact subsets of the plane separate the plane? Couldn´t $K$ in 2) be a "closed ring"? |
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Mar 8 |
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Topological spaces determined by generalized metric spaces added example |
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Mar 8 |
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Topological spaces determined by generalized metric spaces @Marcos: The $X$ in my answer is the Arens space (usually denoted by $\mathcal{S}_2$), the one given in Wikipedia is the Arens-Fort space which is a (non-open as you point out) subspace of Arens space. Arens-Fort space is not sequential, while Arens space is sequential but not Frechet. |
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Mar 7 |
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Topological characterization of the closed interval $[0,1]$. @Liviu: Maybe you want to add "connected" to the definition of $eT$. Otherwise the Cantor space with any two points gives another idempotent. |
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Mar 7 |
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Topological characterization of the closed interval $[0,1]$. @Martin/Ali: I guess one could use the van Dalen-Wattel topological characterization of ordered spaces to get rid of $<$. |
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Mar 7 |
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A question from Arhangel’skii-Buzyakova Yes that´s right, but then also the claims that ⋂μ=H and that $H$ is a $G_{2^\omega}$-set in $Z$ are not justified. |
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Mar 7 |
accepted | A question from Arhangel’skii-Buzyakova |
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Mar 6 |
answered | A question from Arhangel’skii-Buzyakova |
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Mar 6 |
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Adding a random real makes the set of ground model reals meager It is Theorem 3.20 in Kunen´s article, which also proves (at once) that after adding a Cohen real, the ground model reals become null. |
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Mar 5 |
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On the notion of partial semigroup The assertion $\forall x [p(x) \lor q(x) \implies r(x)]$ is equivalent to the conjunction of $\forall x [p(x) \implies r(x)]$ and $\forall x [q(x) \implies r(x)]$ not to their disjunction. |
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Mar 5 |
revised |
On the notion of partial semigroup fixed broken link |
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Mar 5 |
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On the notion of partial semigroup You mean "conjunctive combination"? Also, the algebraic definition of groupoid (which is equivalent to the cat definition according to en.wikipedia.org/wiki/Groupoid#Algebraic) has the same associativity notion as Exel´s notion. |
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Mar 5 |
answered | On the notion of partial semigroup |
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Feb 27 |
revised |
Is there a compact space with no countably generated dense subspace? Update after answer and comments |
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Feb 27 |
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Is there a compact space with no countably generated dense subspace? Santi, \omega^* was my first guess too, but I don´t know how to prove it. |
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Feb 27 |
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Definition of ordered set which split into two isomorphics ordered sets The order is an idempotent with respect to the sum of linear orders. |
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Feb 26 |
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Is there a compact space with no countably generated dense subspace? That is very nice Santi! thanks! |
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Feb 26 |
asked | Is there a compact space with no countably generated dense subspace? |
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Feb 23 |
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Which topological spaces are (topological) groups? A first countable topological group is metrizable. A compact group is hereditarily Lindelof iff it is hereditarily separable iff it is metrizable. As for the question, I remember reading about it in some paper by Jan van Mill, but can't remember which; anyway there wasn't anything else to read about it, it was just a comment towards the end of the paper (if I remember correctly). |
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Feb 23 |
answered | Which topological spaces are (topological) groups? |
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Feb 20 |
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Non-principal ultrafilters on ω To show the existence of such colouring it is enough to assume the existence of a non-meager filter on $\omega$. There are models with non-meager filters and with no ultrafilters. |
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Feb 20 |
accepted | Is the Sorgenfrey Line monotonically monolithic? |
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Feb 19 |
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A linear order obtained by forcing with P(omega)/fin @Asaf: In "Happy families" Mathias showed that $\omega \to (\omega)^\omega$ is consistent with ZF+DC (provided that there are inaccessibles). According to Di Prisco (in "Partitions of the reals in models of ZF"), Mathias´ result actually "establishes that $\omega \to (\omega)^\omega$ holds in Solovay models". |
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Feb 19 |
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A linear order obtained by forcing with P(omega)/fin @Asaf: they only use that the ground model satisfies ZF and the partition relation $\omega \to (\omega)^\omega$. |
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Feb 19 |
answered | Is the Sorgenfrey Line monotonically monolithic? |
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Feb 13 |
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Is there a co-Hahn-Mazurkiewicz theorem for line-filling spaces? There are no "MINIMAL line-filling spaces". If $f:X \to [0,1]$ is onto then $f^{-1}([0,1/2])$ is a proper line-filling subspace of $X$. |
