The ω-problem

Stanisław Kowalczyk

Displaying similar documents to “The ω-problem”

Selection principles and upper semicontinuous functions

Masami Sakai (2009)

Colloquium Mathematicae

Similarity:

In connection with a conjecture of Scheepers, Bukovský introduced properties wQN* and SSP* and asked whether wQN* implies SSP*. We prove it in this paper. We also give characterizations of properties S₁(Γ,Ω) and $S_{f i n} (Γ, Ω)$ in terms of upper semicontinuous functions

A note on $R_{0}$ -topological spaces

K. K. Dube (1974)

Matematički Vesnik

Similarity:

On topological groups with a small base and metrizability

Saak Gabriyelyan, Jerzy Kąkol, Arkady Leiderman (2015)

Fundamenta Mathematicae

Similarity:

A (Hausdorff) topological group is said to have a -base if it admits a base of neighbourhoods of the unit, $U_{α} : α \in ℕ^{ℕ}$ , such that $U_{α} \subset U_{β}$ whenever β ≤ α for all $α, β \in ℕ^{ℕ}$ . The class of all metrizable topological groups is a proper subclass of the class $T G_{}$ of all topological groups having a -base. We prove that a topological group is metrizable iff it is Fréchet-Urysohn and has a -base. We also show that any precompact set in a topological group $G \in T G_{}$ is metrizable, and hence G is strictly angelic. We deduce from...

On Grosswald's conjecture on primitive roots

Stephen D. Cohen, Tomás Oliveira e Silva, Tim Trudgian (2016)

Acta Arithmetica

Similarity:

Grosswald’s conjecture is that g(p), the least primitive root modulo p, satisfies g(p) ≤ √p - 2 for all p > 409. We make progress towards this conjecture by proving that g(p) ≤ √p -2 for all $409 < p < 2.5 \times 10^{15}$ and for all $p > 3.38 \times 10^{71}$ .

Extremely primitive groups and linear spaces

Haiyan Guan, Shenglin Zhou (2016)

Czechoslovak Mathematical Journal

Similarity:

A non-regular primitive permutation group is called extremely primitive if a point stabilizer acts primitively on each of its nontrivial orbits. Let $𝒮$ be a nontrivial finite regular linear space and $G \leq Aut (𝒮) .$ Suppose that $G$ is extremely primitive on points and let rank $(G)$ be the rank of $G$ on points. We prove that rank $(G) \geq 4$ with few exceptions. Moreover, we show that $Soc (G)$ is neither a sporadic group nor an alternating group, and $G = PSL (2, q)$ with $q + 1$ a Fermat prime if $Soc (G)$ is a finite classical simple group. ...

Lower semicontinuous envelopes in $W^{1, 1} \times L^{p}$

Ana Margarida Ribeiro, Elvira Zappale (2014)

Banach Center Publications

Similarity:

The lower semicontinuity of functionals of the type $\int_{Ω} f (x, u, v, \nabla u) d x$ with respect to the $(W^{1, 1} \times L^{p})$ -weak* topology is studied. Moreover, in absence of lower semicontinuity, an integral representation in $W^{1, 1} \times L^{p}$ for the lower semicontinuous envelope is also provided.

On the Hausdorff Dimension of Topological Subspaces

Tomasz Szarek, Maciej Ślęczka (2006)

Bulletin of the Polish Academy of Sciences. Mathematics

Similarity:

It is shown that every Polish space X with $d i m_{T} X \geq d$ admits a compact subspace Y such that $d i m_{H} Y \geq d$ where $d i m_{T}$ and $d i m_{H}$ denote the topological and Hausdorff dimensions, respectively.

Growth of a primitive of a differential form

Jean-Claude Sikorav (2001)

Bulletin de la Société Mathématique de France

Similarity:

For an exact differential form on a Riemannian manifold to have a primitive bounded by a given function $f$ , by Stokes it has to satisfy some weighted isoperimetric inequality. We show the converse up to some constants if $M$ has bounded geometry. For a volume form, it suffices to have the inequality ( $| Ω | \leq \int_{\partial Ω} f d σ$ for every compact domain $Ω \subset M$ ). This implies in particular the “well-known” result that if $M$ is the universal covering of a compact Riemannian manifold with non-amenable fundamental group, then...

Minimax theorems without changeless proportion

Liang-Ju Chu, Chi-Nan Tsai (2003)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Similarity:

The so-called minimax theorem means that if X and Y are two sets, and f and g are two real-valued functions defined on X×Y, then under some conditions the following inequality holds: $i n f_{y \in Y} s u p_{x \in X} f (x, y) \leq s u p_{x \in X} i n f_{y \in Y} g (x, y)$ . We will extend the two functions version of minimax theorems without the usual condition: f ≤ g. We replace it by a milder condition: $s u p_{x \in X} f (x, y) \leq s u p_{x \in X} g (x, y)$ , ∀y ∈ Y. However, we require some restrictions; such as, the functions f and g are jointly upward, and their upper sets are connected. On the other hand, by using some...

On $R_{0}$ and $R_{1}$ topological spaces

D. Janković (1981)

Matematički Vesnik

Similarity:

$R_{0}$ and $R_{1}$ topological spaces

C. Dorsett (1978)

Matematički Vesnik

Similarity:

A note on $R_{0}$ and $R_{1}$ topological spaces

M. R. Žižović (1986)

Matematički Vesnik

Similarity:

Nonnormality of remainders of some topological groups

Aleksander V. Arhangel&#039;skii, J. van Mill (2016)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

It is known that every remainder of a topological group is Lindelöf or pseudocompact. Motivated by this result, we study in this paper when a topological group $G$ has a normal remainder. In a previous paper we showed that under mild conditions on $G$ , the Continuum Hypothesis implies that if the Čech-Stone remainder $G^{*}$ of $G$ is normal, then it is Lindelöf. Here we continue this line of investigation, mainly for the case of precompact groups. We show that no pseudocompact group, whose weight...