On the density and net weight of regular spaces

Armando Romero Morales

Displaying similar documents to “On the density and net weight of regular spaces”

Internally club and approachable for larger structures

John Krueger (2008)

Fundamenta Mathematicae

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We generalize the notion of a fat subset of a regular cardinal κ to a fat subset of $P_{κ} (X)$ , where κ ⊆ X. Suppose μ < κ, $μ^{< μ} = μ$ , and κ is supercompact. Then there is a generic extension in which κ = μ⁺⁺, and for all regular λ ≥ μ⁺⁺, there are stationarily many N in ${[H (λ)]}^{μ ⁺}$ which are internally club but not internally approachable.

On the asymptotics of counting functions for Ahlfors regular sets

Dušan Pokorný, Marc Rauch (2022)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the so-called Ahlfors regular sets (also known as $s$ -regular sets) in metric spaces. First we show that those sets correspond to a certain class of tree-like structures. Building on this observation we then study the following question: Under which conditions does the limit ${lim}_{ε \to 0 +} ε^{s} N (ε, K)$ exist, where $K$ is an $s$ -regular set and $N (ε, K)$ is for instance the $ε$ -packing number of $K$ ?

The Gibbs phenomenon and Lebesgue constants for regular $A (λ)$ means

V. Swaminathan (1977)

Matematički Vesnik

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Nonnormality points of βX∖X

William Fleissner, Lynne Yengulalp (2011)

Fundamenta Mathematicae

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Let X be a crowded metric space of weight κ that is either $κ^{ω}$ -like or locally compact. Let y ∈ βX∖X and assume GCH. Then a space of nonuniform ultrafilters embeds as a closed subspace of (βX∖X)∖y with y as the unique limit point. If, in addition, y is a regular z-ultrafilter, then the space of nonuniform ultrafilters is not normal, and hence (βX∖X)∖y is not normal.

Unit-regularity and representability for semiartinian $*$ -regular rings

Christian Herrmann (2020)

Archivum Mathematicum

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We show that any semiartinian $*$ -regular ring $R$ is unit-regular; if, in addition, $R$ is subdirectly irreducible then it admits a representation within some inner product space.

Universal completely regular dendrites

K. Omiljanowski, S. Zafiridou (2005)

Colloquium Mathematicae

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We define a dendrite $E_{n}$ which is universal in the class of all completely regular dendrites with order of points not greater than n. In particular, the dendrite $E_{ω}$ is universal in the class of all completely regular dendrites. The construction starts with the standard universal dendrite $D_{n}$ of order n described by J. J. Charatonik.

Inequalities for a regular polygon in $L^{p}$ spaces

M. Pavlović (1992)

Matematički Vesnik

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Supercompactness and failures of GCH

Sy-David Friedman, Radek Honzik (2012)

Fundamenta Mathematicae

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Let κ < λ be regular cardinals. We say that an embedding j: V → M with critical point κ is λ-tall if λ < j(κ) and M is closed under κ-sequences in V. Silver showed that GCH can fail at a measurable cardinal κ, starting with κ being κ⁺⁺-supercompact. Later, Woodin improved this result, starting from the optimal hypothesis of a κ⁺⁺-tall measurable cardinal κ. Now more generally, suppose that κ ≤ λ are regular and one wishes the GCH to fail at λ with κ being λ-supercompact. Silver’s...

Reflecting character and pseudocharacter

Lucia R. Junqueira, Alberto M. E. Levi (2015)

Commentationes Mathematicae Universitatis Carolinae

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We say that a cardinal function $φ$ reflects an infinite cardinal $κ$ , if given a topological space $X$ with $φ (X) \geq κ$ , there exists $Y \in {[X]}^{\leq κ}$ with $φ (Y) \geq κ$ . We investigate some problems, discussed by Hodel and Vaughan in Reflection theorems for cardinal functions, Topology Appl. 100 (2000), 47–66, and Juhász in Cardinal functions and reflection, Topology Atlas Preprint no. 445, 2000, related to the reflection for the cardinal functions character and pseudocharacter. Among other results, we present some new equivalences...

Regular coordinates and reduction of deformation equations for Fuchsian systems

Yoshishige Haraoka (2012)

Banach Center Publications

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For a Fuchsian system $d Y / d x = (\sum_{j =}^{p} (A_{j}) / (x - t_{j})) Y$ , (F) $t ₁, t ₂, . . ., t_{p}$ being distinct points in ℂ and $A ₁, A ₂, . . ., A_{p} \in M (n \times n; ℂ)$ , the number α of accessory parameters is determined by the spectral types $s (A ₀), s (A ₁), . . ., s (A_{p})$ , where $A ₀ = - \sum_{j = 1}^{p} A_{j}$ . We call the set $z = (z ₁, z ₂, . . ., z_{α})$ of α parameters a regular coordinate if all entries of the $A_{j}$ are rational functions in z. It is not yet known that, for any irreducibly realizable set of spectral types, a regular coordinate does exist. In this paper we study a process of obtaining a new regular coordinate from a given one by a coalescence of eigenvalues...

Locally Σ₁-definable well-orders of H(κ⁺)

Peter Holy, Philipp Lücke (2014)

Fundamenta Mathematicae

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Given an uncountable cardinal κ with $κ = κ^{< κ}$ and $2^{κ}$ regular, we show that there is a forcing that preserves cofinalities less than or equal to $2^{κ}$ and forces the existence of a well-order of H(κ⁺) that is definable over ⟨H(κ⁺),∈⟩ by a Σ₁-formula with parameters. This shows that, in contrast to the case "κ = ω", the existence of a locally definable well-order of H(κ⁺) of low complexity is consistent with failures of the GCH at κ. We also show that the forcing mentioned above introduces a Bernstein...

Initially $κ$ -compact spaces for large $κ$

Stavros Christodoulou (1999)

Commentationes Mathematicae Universitatis Carolinae

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This work presents some cardinal inequalities in which appears the closed pseudo-character, $ψ_{c}$ , of a space. Using one of them — $ψ_{c} (X) \leq 2^{d (X)}$ for $T_{2}$ spaces — we improve, from $T_{3}$ to $T_{2}$ spaces, the well-known result that initially $κ$ -compact $T_{3}$ spaces are $λ$ -bounded for all cardinals $λ$ such that $2^{λ} \leq κ$ . And then, using an idea of A. Dow, we prove that initially $κ$ -compact $T_{2}$ spaces are in fact compact for $κ = 2^{F (X)}$ , $2^{s (X)}$ , $2^{t (X)}$ , $2^{χ (X)}$ , $2^{ψ_{c} (X)}$ or $κ = max {τ^{+}, τ^{< τ}}$ , where $τ > t (p, X)$ for all $p \in X$ .

On ordinals accessible by infinitary languages

Saharon Shelah, Pauli Väisänen, Jouko Väänänen (2005)

Fundamenta Mathematicae

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Let λ be an infinite cardinal number. The ordinal number δ(λ) is the least ordinal γ such that if ϕ is any sentence of $L_{λ ⁺ ω}$ , with a unary predicate D and a binary predicate ≺, and ϕ has a model ℳ with $⟨ D^{ℳ}, ≺^{ℳ} ⟩$ a well-ordering of type ≥ γ, then ϕ has a model ℳ ’ where $⟨ D^{ℳ^{'}}, ≺^{ℳ^{'}} ⟩$ is non-well-ordered. One of the interesting properties of this number is that the Hanf number of $L_{λ ⁺ ω}$ is exactly $ℶ_{δ (λ)}$ . It was proved in [BK71] that if ℵ₀ < λ < κ $a r e r e g u l a r c a r d i n a l n u m b e r s, t h e n t h e r e i s a f o r c i n g e x t e n s i o n, p r e s e r v i n g c o f i n a l i t i e s, s u c h t h a t i n t h e e x t e n s i o n$ 2λ = κ $a n d δ (λ) < λ ⁺ ⁺ . W e i m p r o v e t h i s r e s u l t b y p r o v i n g t h e f o l l o w i n g : S u p p o s e ℵ ₀ < λ < θ \leq κ a r e c a r d i n a l n u m b e r s s u c h t h a t$ ∙ $λ^{< λ} = λ$ ; ∙ cf(θ) ≥ λ⁺ and $μ^{λ} < θ$ whenever μ < θ; ∙ $κ^{λ} = κ$ . Then there...

Assertion Q distinguishes topologically ω* and $𝔪$ when $𝔪$ regular and $𝔪 > ω$

R. Frankiewicz (1978)

Colloquium Mathematicae

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