A note on semitopological groups and paratopological groups

Peng, Liang-Xue

doi:10.1016/j.topol.2015.06.001

Cited by 3 publications

(2 citation statements)

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“…From a different viewpoint, this question has attracted the interest of many researchers recently (cf. [18,21,22,24,25,26,27,30]) and, to some extent, our motivation for 2010 Mathematics Subject Classification. Primary: 54B30, 18B30, 54D10; Secondary: 54H10, 22A30 Key Words and Phrases: Topological algebraic structure, Epireflection, Separation axiom, Mal'tsev spaces .…”

Section: Introductionmentioning

confidence: 99%

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Reflections in topological algebraic structures

Hernández-Arzusa

Hernández

2020

Topology and its Applications

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Let C be an epireflective category of Top and let r C be the epireflective functor associated with C. If A denotes a (semi)topological algebraic subcategory of Top, we study when r C (A) is an epireflective subcategory of A. We prove that this is always the case for semi-topological structures and we find some sufficient conditions for topological algebraic structures. We also study when the epireflective functor preserves products, subspaces and other properties. In particular, we solve an open question about the coincidence of epireflections proposed by Echi and Lazaar in [6, Question 1.6] and repeated in [7, Question 1.9]. Finally, we apply our results in different specific topological algebraic structures. 2 J. HERNÁNDEZ-ARZUSA AND S. HERNÁNDEZ this research has been to give a unified approach to this topic. First, we recall some definitions and basic facts. A full subcategory A of a category B is reflective if the canonical embedding of A in B has a left adjoint r A : B −→ A (called reflection). Thus for each B-object B there exists an A-object r A B and and a B-morphism r (B,A) : B → r A B such that for each B-morphism f : B → A to an A-object A, there exists a unique A-morphism f : r A B → A such that the following diagram commutes B r (B,A)The pair (r A B, r (B,A) ) is called the A-reflection of B and the morphism r (B,A) is called A-reflection arrow. If all A-reflection arrows are epimorphisms, then the subcategory A is said to be epireflective. The functor r: B → A, which is called the reflector, assigns to each B-morphism f : X −→ Y , the A-morphism r A (f ) that is determined by the following commutative diagram

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Section: Introductionmentioning

confidence: 99%

“…From a different viewpoint, this question has attracted the interest of many researchers recently (cf. [18,21,22,24,25,26,27,30]) and, to some extent, our motivation for this research has been to give a unified approach to this topic. First, we recall some definitions and basic facts.…”

Section: Introductionmentioning

confidence: 99%