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Semi-quotient mappings and spaces

Moiz ud Din Khan, Rafaqat Noreen, Muhammad Siddique Bosan (2016)

Open Mathematics

In this paper, we continue the study of s-topological and irresolute-topological groups. We define semi-quotient mappings which are stronger than semi-continuous mappings, and then consider semi-quotient spaces and groups. It is proved that for some classes of irresolute-topological groups (G, *, τ) the semi-quotient space G/H is regular. Semi-isomorphisms of s-topological groups are also discussed.

Separation properties for self-conformal sets

Yuan-Ling Ye (2002)

Studia Mathematica

For a one-to-one self-conformal contractive system w j j = 1 m on ℝ d with attractor K and conformality dimension α, Peres et al. showed that the open set condition and strong open set condition are both equivalent to 0 < ℋ α ( K ) < ∞ . We give a simple proof of this result as well as discuss some further properties related to the separation condition.

Separation properties in congruence lattices of lattices

Miroslav Ploščica (2000)

Colloquium Mathematicae

We investigate the congruence lattices of lattices in the varieties ℳ n . Our approach is to represent congruences by open sets of suitable topological spaces. We introduce some special separation properties and show that for different n the lattices in ℳ n have different congruence lattices.

Sequence entropy pairs and complexity pairs for a measure

Wen Huang, Alejandro Maass, Xiangdong Ye (2004)

Annales de l’institut Fourier

In this paper we explore topological factors in between the Kronecker factor and the maximal equicontinuous factor of a system. For this purpose we introduce the concept of sequence entropy n -tuple for a measure and we show that the set of sequence entropy tuples for a measure is contained in the set of topological sequence entropy tuples [H- Y]. The reciprocal is not true. In addition, following topological ideas in [BHM], we introduce a weak notion and a strong notion of complexity pair for a...

Sequential continuity on dyadic compacta and topological groups

Aleksander V. Arhangel'skii, Winfried Just, Grzegorz Plebanek (1996)

Commentationes Mathematicae Universitatis Carolinae

We study conditions under which sequentially continuous functions on topological spaces and sequentially continuous homomorphisms of topological groups are continuous.

Sequential convergences on Boolean algebras defined by systems of maximal filters

Roman Frič, Ján Jakubík (2001)

Czechoslovak Mathematical Journal

We study sequential convergences defined on a Boolean algebra by systems of maximal filters. We describe the order properties of the system of all such convergences. We introduce the category of 2-generated convergence Boolean algebras and generalize the construction of Novák sequential envelope to such algebras.

Sequential convergences on free lattice ordered groups

Ján Jakubík (1992)

Mathematica Bohemica

In this paper the partially ordered set Conv G of all sequential convergences on G is investigated, where G is either a free lattice ordered group or a free abelian lattice ordered group.

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