The Epireflective Hull of the Category of T 1 Dispersed Spaces

1980 ◽  
Vol 80 (2) ◽  
pp. 306
Author(s):  
V. Neumann-Lara ◽  
R. G. Wilson
Keyword(s):  
Epireflective Hull

scholarly journals On the epireflective hull of Top in Near

2006 ◽  
Vol 153 (16) ◽  
pp. 3071-3084 ◽  
Author(s):  
H.L. Bentley ◽  
John W. Carlson ◽  
H. Herrlich
Keyword(s):  
Epireflective Hull

scholarly journals The epireflective hull of the category of $T\sb{1}$ dispersed spaces

1980 ◽  
Vol 80 (2) ◽  
pp. 306-306
Author(s):  
V. Neumann Lara ◽  
R. G. Wilson
Keyword(s):  
Epireflective Hull

On the Epireflective Hull of Topological Nearness Groups in the Category of Nearness Groups

2007 ◽  
Vol 30 (4) ◽  
pp. 499-505
Author(s):  
Lamar H. Bentley ◽  
Vijaya L. Gompa
Keyword(s):  
Epireflective Hull

Hölder categories

2014 ◽  
Vol 64 (3) ◽  
Author(s):  
Anthony Hager ◽  
Jorge Martínez
Keyword(s):  
Order Unit ◽  
Real Numbers ◽  
Initial Element ◽  
Ordered Groups ◽  
Lattice Ordered Groups ◽  
Terminal Object ◽  
Epireflective Hull ◽  
Strong Order ◽  
Archimedean Lattice ◽  
Initial Object

AbstractHölder categories are invented to provide an axiomatic foundation for the study of categories of archimedean lattice-ordered algebraic structures. The basis of such a study is Hölder’s Theorem (1908), stating that the archimedean totally ordered groups are precisely the subgroups of the additive real numbers ℝ with the usual addition and ordering, which remains the single most consequential result in the studies of lattice-ordered algebraic systems since Birkhoff and Fuchs to the present.This study originated with interest in W*, the category of all archimedean lattice-ordered groups with a designated strong order unit, and the ℓ-homomorphisms which preserve those units, and, more precisely, with interest in the epireflections on W*. In the course of this study, certain abstract notions jumped to the forefront. Two of these, in particular, seem to have been mostly overlooked; some notion of simplicity appears to be essential to any kind of categorical study of W*, as are the quasi-initial objects in a category. Once these two notions have been brought into the conversation, a Hölder category may then be defined as one which is complete, well powered, and in which(a) the initial object I is simple, and(b) there is a simple quasi-initial coseparator R.In this framework it is shown that the epireflective hull of R is the least monoreflective class. And, when I = R — that is, the initial element is simple and a coseparator — a theorem of Bezhanishvili, Morandi, and Olberding, for bounded archimedean f-algebras with identity, can be be generalized, as follows: for any Hölder category subject to the stipulation that the initial object is a simple coseparator, every uniformly nontrivial reflection — meaning that the reflection of each non-terminal object is non-terminal — is a monoreflection.Also shown here is the fact that the atoms in the class of epireflective classes are the epireflective hulls of the simple quasi-initial objects. From this observation one easily deduces a converse to the result of Bezhanishvili, Morandi, and Olberding: if in a Hölder category every epireflection is a monoreflection, then the initial object is a coseparator.

FTS0: The epireflective hull of the Sierpinski object in FTS

1989 ◽  
Vol 29 (2) ◽  
pp. 171-176 ◽  
Author(s):  
R. Lowen ◽  
Arun K. Srivastava
Keyword(s):  
Epireflective Hull
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