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We define an ultra $L I$ -ideal of a lattice implication algebra and give equivalent conditions for an $L I$ -ideal to be ultra. We show that every subset of a lattice implication algebra which has the finite additive property can be extended to an ultra $L I$ -ideal.

Ultra $L I$ -Ideals in lattice implication algebras and $M T L$ -algebras

Xiaohong Zhang, Ke Yun Qin, Wiesław Aleksander Dudek (2007)

Czechoslovak Mathematical Journal

A mistake concerning the ultra $L I$ -ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an $L I$ -ideal to be an ultra $L I$ -ideal are given. Moreover, the notion of an $L I$ -ideal is extended to $M T L$ -algebras, the notions of a (prime, ultra, obstinate, Boolean) $L I$ -ideal and an $I L I$ -ideal of an $M T L$ -algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in $M T L$ -algebra: (1) prime proper $L I$ -ideal and Boolean $L I$ -ideal,...

Ultracompanions of subsets of a group

I. Protasov, S. Slobodianiuk (2014)

Commentationes Mathematicae Universitatis Carolinae

Let $G$ be a group, $β G$ be the Stone-Čech compactification of $G$ endowed with the structure of a right topological semigroup and $G^{*} = β G ∖ G$ . Given any subset $A$ of $G$ and $p \in G^{*}$ , we define the $p$ -companion $Δ_{p} (A) = A^{*} \cap G p$ of $A$ , and characterize the subsets with finite and discrete ultracompanions.

Ultrafilter spaces and compactifications.

Salbany, S. (2000)

Portugaliae Mathematica

Ultrafilter with $ℵ_{0}$ predecessors in Rudin-Frolík order

Lev Bukovský, Eva Butkovičová (1981)

Commentationes Mathematicae Universitatis Carolinae

Ultrafilter-limit points in metric dynamical systems

Salvador García-Ferreira, Manuel Sanchis (2007)

Commentationes Mathematicae Universitatis Carolinae

Given a free ultrafilter $p$ on $ℕ$ and a space $X$ , we say that $x \in X$ is the $p$ -limit point of a sequence ${(x_{n})}_{n \in ℕ}$ in $X$ (in symbols, $x = p$ - ${lim}_{n \to \infty} x_{n}$ ) if for every neighborhood $V$ of $x$ , ${n \in ℕ : x_{n} \in V} \in p$ . By using $p$ -limit points from a suitable metric space, we characterize the selective ultrafilters on $ℕ$ and the $P$ -points of $ℕ^{*} = β (ℕ) ∖ ℕ$ . In this paper, we only consider dynamical systems $(X, f)$ , where $X$ is a compact metric space. For a free ultrafilter $p$ on $ℕ^{*}$ , the function $f^{p} : X \to X$ is defined by $f^{p} (x) = p$ - ${lim}_{n \to \infty} f^{n} (x)$ for each $x \in X$ . These functions are not continuous in general. For a...

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Über innere Abbildungen

Über metrische Räume und $𝒞_{c} (X)$

Über offene Abbildungen auf die 3-Sphäre.

Über Peano-Kurven.

Über Richtungsfelder in den projektiven Räumen und einen Satz aus der reellen Algebra.

Ueber D-Minimale Aktionen von Zusammen-Haengenden Lie-Gruppen

Ueber eine Aufgabe aus der Geometria situs

Ueber einen Satz aus der Analysis situs

Ueber einen Satz aus der Theorie der stetigen Mannigfaltigkeiten

Ultra $L I$ -ideals in lattice implication algebras

Ultra $L I$ -Ideals in lattice implication algebras and $M T L$ -algebras

Ultracompanions of subsets of a group

Ultrafilter spaces and compactifications.

Ultrafilter with $ℵ_{0}$ predecessors in Rudin-Frolík order

Ultrafilter-limit points in metric dynamical systems

Ultrafilters and Darboux property of finitely additive measure

Ultrafilters on a discrete set with two binary operations.

Ultrafiltres absolus

Ultrafiltres absolus et problèmes d'extraction de sous-suites

Ultrafiltres sur un espace spectral - Anneaux de Baer - Anneaux a spectre minimal compact.

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