New Proofs of the Consistency of the Normal Moore Space Conjecture I*
نویسندگان
چکیده
The normal Moore space conjecture asserts that normal Moore spaces are metrizable. Nyikos has proven the consistency (from the existence of a strongly compact cardinal) of the conjecture holding and Fleissner has proven that at least a measurable cardinal is needed to prove the consistency. Although extremely elegant, Nyikos’ proof relies on Kunen’s proof of the consistency of the product measure exrension axiom and does not lend itself to other applications. In this paper we first present the groundwork for iterated forcing and reflection type proofs from the assumption of a supercompact cardinal. We then use this technology to give a proof of the normal Moore space conjecture as well as several other similar results which use a variation of the proof.
منابع مشابه
$L^p$-Conjecture on Hypergroups
In this paper, we study $L^p$-conjecture on locally compact hypergroups and by some technical proofs we give some sufficient and necessary conditions for a weighted Lebesgue space $L^p(K,w)$ to be a convolution Banach algebra, where $1<p<infty$, $K$ is a locally compact hypergroup and $w$ is a weight function on $K$. Among the other things, we also show that if $K$ is a locally compact hyper...
متن کاملOn the duality of quadratic minimization problems using pseudo inverses
In this paper we consider the minimization of a positive semidefinite quadratic form, having a singular corresponding matrix $H$. We state the dual formulation of the original problem and treat both problems only using the vectors $x in mathcal{N}(H)^perp$ instead of the classical approach of convex optimization techniques such as the null space method. Given this approach and based on t...
متن کاملON THE CAPACITY OF EILENBERG-MACLANE AND MOORE SPACES
K. Borsuk in 1979, at the Topological Conference in Moscow, introduced concept of the capacity of a compactum and asked some questions concerning properties of the capacity ofcompacta. In this paper, we give partial positive answers to three of these questions in some cases. In fact, by describing spaces homotopy dominated by Moore and Eilenberg-MacLane spaces, the capacities of a Moore space $...
متن کاملThe Constructible Universe
Assuming the axiom of constructibility, points in closed discrete subspaces of certain normal spaces can be simultaneously separated. This is a partial result towards the normal Moore space conjecture. The normal Moore space conjecture states that every normal Moore space is metrizable. This is known to be not provable from the usual axioms of set theory, since Silver [4] shows that Martin's ax...
متن کاملSome notes on ``Common fixed point of two $R$-weakly commuting mappings in $b$-metric spaces"
Very recently, Kuman et al. [P. Kumam, W. Sintunavarat, S. Sedghi, and N. Shobkolaei. Common Fixed Point of Two $R$-Weakly Commuting Mappings in $b$-Metric Spaces. Journal of Function Spaces, Volume 2015, Article ID 350840, 5 pages] obtained some interesting common fixed point results for two mappings satisfying generalized contractive condition in $b$-metric space without the assumption of the...
متن کامل