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Dowker space Whitehead Problem Poset Commutative cancellative semigroups Minimal Walks Sakurai's Bell inequality Singular cardinals combinatorics Vanishing levels Lipschitz reduction Partition relations for trees indecomposable filter Closed coloring Fat stationary set Universal Sequences Coherent tree Square-Brackets Partition Relations polarized partition relation Intersection model Absoluteness Club Guessing Almost Souslin Subadditive Knaster Non-saturation Antichain Successor of Singular Cardinal Forcing Axioms Forcing with side conditions SNR OCA Strong coloring Strongly Luzin set Monotonically far Uniformly coherent Greatly Mahlo club_AD Reduced Power Jonsson cardinal Chang's conjecture tensor product graph Distributive tree free Boolean algebra unbounded function Strongly compact cardinal Generalized Clubs Diamond Mandelbrot set Uniformization 54G20 weak Kurepa tree Well-behaved magma Prevalent singular cardinals Reflecting stationary set Partition Relations coloring number Respecting tree Erdos-Hajnal graphs L-space Sigma-Prikry strongly bounded groups full tree Subtle cardinal Fast club Analytic sets PFA(S)[S] incompactness Cardinal function transformations Ascending path Small forcing P-Ideal Dichotomy Diamond for trees Erdos Cardinal square principles Parameterized proxy principle Nonspecial tree Rock n' Roll projective Boolean algebra Amenable C-sequence diamond star Luzin set Singular cofinality Ascent Path Sierpinski's onto mapping principle Subtle tree property O-space Ramsey theory over partitions Hedetniemi's conjecture very good scale Kurepa Hypothesis specializable Souslin tree Shelah's Strong Hypothesis weak diamond middle diamond Diamond-sharp b-scale Commutative projection system stick Iterated forcing Constructible Universe Souslin Tree Generalized descriptive set theory Was Ulam right? Hereditarily Lindelöf space Precaliber Ineffable cardinal Dushnik-Miller Aronszajn tree Postprocessing function stationary reflection ZFC construction Hindman's Theorem Singular Density Cardinal Invariants Selective Ultrafilter positive partition relation Entangled linear order free Souslin tree Ostaszewski square xbox C-sequence Cohen real Countryman line Rainbow sets GMA Axiom R Large Cardinals Local Club Condensation. Prikry-type forcing Foundations higher Baire space Open Access PFA countably metacompact S-Space Forcing Uniformly homogeneous Almost-disjoint family weak square Chromatic number Microscopic Approach square sap Martin's Axiom super-Souslin tree Successor of Regular Cardinal Knaster and friends stationary hitting approachability ideal Weakly compact cardinal Slim tree Interval topology on trees HOD nonmeager set Filter reflection AIM forcing Ulam matrix Subnormal ideal regressive Souslin tree perfectly normal reflection principles ccc Fodor-type reflection Rado's conjecture Almost countably chromatic
Tag Archives: Hereditarily Lindelöf space
The S-space problem, and the cardinal invariant $\mathfrak p$
Recall that an $S$-space is a regular hereditarily separable topological space which is not hereditarily Lindelöf. Do they exist? Consistently, yes. However, Szentmiklóssy proved that compact $S$-spaces do not exist, assuming Martin’s Axiom. Pushing this further, Todorcevic later proved that … Continue reading
Posted in Blog, Expository, Open Problems
Tagged Cardinal Invariants, Hereditarily Lindelöf space, P-Ideal Dichotomy, PFA(S)[S], S-Space
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On topological spaces of singular density and minimal weight
Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … Continue reading
Workshop on Set Theory and its Applications, February 2007
These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … Continue reading
Infinite Combinatorial Topology
Back in 2005, as a master student, I attended a course by Boaz Tsaban, entitled “Infinite Combinatorial Topology”. A friend and I decided to produce lecture notes, but in a somewhat loose sense, that is: we sometimes omit material given … Continue reading
Posted in Notes
Tagged b-scale, Cardinal function, Cardinal Invariants, Hereditarily Lindelöf space
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