### Archives

### Recent blog posts

- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013
- Gabriel Belachsan (14/5/1976 – 20/8/2013) August 20, 2013

### Keywords

Forcing middle diamond incompactness Aronszajn tree Generalized Clubs projective Boolean algebra Dushnik-Miller Knaster Antichain Martin's Axiom Successor of Regular Cardinal Almost-disjoint famiy Absoluteness S-Space Square-Brackets Partition Relations Singular Cofinality free Boolean algebra Rado's conjecture OCA sap b-scale Successor of Singular Cardinal Cardinal Invariants Rainbow sets very good scale Cohen real Ostaszewski square Hedetniemi's conjecture Singular Density Cardinal function diamond star Kurepa Hypothesis Forcing Axioms ccc Chromatic number Shelah's Strong Hypothesis weak square approachability ideal Universal Sequences L-space Diamond Erdos Cardinal Non-saturation Erdos-Hajnal graphs Prevalent singular cardinals Foundations Almost countably chromatic Small forcing Poset Rock n' Roll Axiom R stationary hitting PFA(S)[S] P-Ideal Dichotomy tensor product graph Club Guessing polarized partition relation Souslin Tree Whitehead Problem PFA Hereditarily Lindelöf space Sakurai's Bell inequality reflection principles Partition Relations Constructible Universe weak diamond Minimal Walks Singular cardinals combinatorics Weakly compact cardinal Prikry-type forcing Uniformization stationary reflection Mandelbrot set Large Cardinals square

# 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 Hereditarily Lindelöf space, P-Ideal Dichotomy, PFA(S)[S], S-Space
3 Comments

## 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

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
Leave a comment