Functorial polar functions

2011 ◽  
Vol 61 (3) ◽  
Author(s):  
Ricardo Carrera
Keyword(s):  
Hausdorff Spaces ◽  
Weak Unit ◽  
Closed Sets ◽  
Polar Function ◽  
Uncountable Cardinal ◽  
Functorial Polar Functions ◽  
Skeletal Maps ◽  
Polar Functions ◽  
Regular Closed

AbstractW∞ denotes the category of archimedean ℓ-groups with designated weak unit and complete ℓ-homomorphisms that preserve the weak unit. CmpT2,∞ denotes the category of compact Hausdorff spaces with continuous skeletal maps. This work introduces the concept of a functorial polar function on W∞ and its dual a functorial covering function on CmpT2,∞.We demonstrate that functorial polar functions give rise to reflective hull classes in W ∞ and that functorial covering functions give rise to coreflective covering classes in CmpT 2,∞. We generate a variety of reflective and coreflecitve subcategories and prove that for any regular uncountable cardinal α, the class of α-projectable ℓ-groups is reflective in W ∞, and the class of α-disconnected compact Hausdorff spaces is coreflective in CmpT 2,∞. Lastly, the notion of a functorial polar function (resp. functorial covering function) is generalized to sublattices of polars (resp. sublattices of regular closed sets).

scholarly journals Characterizations of s-closed Hausdorff spaces

1991 ◽  
Vol 51 (2) ◽  
pp. 300-304
Author(s):  
Takashi Noiri
Keyword(s):  
Topological Space ◽  
Hausdorff Spaces ◽  
Closed Sets ◽  
Regular Closed

A topological space X is said to be S-closed if every cover of X by regular closed sets of X has a finite subcover. In this note some characterizations of S-closed Hausdorff spaces are obtained.

scholarly journals On coabsolute paracompact spaces

1979 ◽  
Vol 27 (2) ◽  
pp. 248-256 ◽  
Author(s):  
Catherine L. Gates
Keyword(s):  
Boolean Algebra ◽  
Boolean Algebras ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Algebra Isomorphism ◽  
Closed Sets ◽  
Local Finiteness ◽  
Paracompact Spaces ◽  
Regular Closed

AbstractWe are interested in determining whether two spaces are coabsolute by comparing their Boolean algebras of regular closed sets. It is known that when the spaces are compact Hausdorff they are coabsolute precisely when the Boolean algebras of regular closed sets are isomorphic; but in general this condition is not strong enough to insure that the spaces be coabsolute. In this paper we show that for paracompact Hausdorff spaces, the spaces are coabsolute when the Boolean algebra isomorphism and its inverse ‘preserve’ local finiteness, and for locally compact paracompact Hausdorff spaces, the spaces are coabsolute when the collections of compact regular closed subsets are ‘isomorphic’.

A Measure Theoretical Version of the Aleksandrov Theorem

2008 ◽  
Vol 15 (1) ◽  
pp. 53-61
Author(s):  
Majid Gazor
Keyword(s):  
Borel Measure ◽  
Measure Theory ◽  
Ordinal Number ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Closed Sets

Abstract In this paper a theorem analogous to the Aleksandrov theorem is presented in terms of measure theory. Furthermore, we introduce the condensation rank of Hausdorff spaces and prove that any ordinal number is associated with the condensation rank of an appropriate locally compact totally imperfect space. This space is equipped with a probability Borel measure which is outer regular, vanishes at singletons, and is also inner regular in the sense of closed sets.

On Product of Radón Measures

1969 ◽  
Vol 12 (4) ◽  
pp. 427-444 ◽  
Author(s):  
M. C. Godfrey ◽  
M. Sion
Keyword(s):  
Direct Reference ◽  
Outer Measure ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Radon Measures ◽  
Closed Sets

Let X, Y be locally compact Hausdorff spaces and μ, ν be Radón outer measures on X and Y respectively. The classical product outer measure ϕ on X × Y generated by measurable rectangles, without direct reference to the topology, turns out to have some serious drawbacks. For example, one can only prove that closed sets (and hence Baire sets) are ϕ-measurable. It is unknown, even when X and Y are compact, whether closed sets are ϕ-measurable.

Weakly Generalized Star Pre Regular Closed Sets In Topology

2019 ◽  
Vol 65 (5) ◽  
pp. 1-8
Author(s):  
Vijayalaksmi V ◽  
Senthilkumaran V ◽  
Palaniappan Y
Keyword(s):  
Closed Sets ◽  
Regular Closed

scholarly journals Generalized Binary Regular Closed Sets

2016 ◽  
Vol 4 (2) ◽  
pp. 259
Author(s):  
S. Nithyanantha Jothi ◽  
P. Thangavelu
Keyword(s):  
Basic Properties ◽  
Closed Sets ◽  
Binary Structure ◽  
Regular Closed

<div><p><em>Recently the authors introduced the concept of binary topology between two sets and investigate its basic properties where a binary topology from X to Y is a binary structure satisfying certain axioms that are analogous to the axioms of topology. In this paper we introduce and study generalized binary regular closed sets.</em></p></div>

Soft multi generalized regular sets in soft multi topological spaces

2017 ◽  
Vol 8 (1) ◽  
pp. 9
Author(s):  
Alkan ÖZKAN
Keyword(s):  
Topological Spaces ◽  
Closed Set ◽  
Basic Properties ◽  
Closed Sets ◽  
New Class ◽  
Basic Concepts ◽  
Regular Sets ◽  
Regular Closed

Many researchers have identified some of the basic concepts in soft multi topology and many properties were investigated. The main objective of this study is to provide and study a new class of soft multi closed sets like soft multi generalized regular closed (briefly soft mgr-closed) set and to investigated some of its basic properties in soft multi topological spaces. Furthermore, soft multi α-closed set, soft multi pre-closed set, soft multi semi-closed set, soft multi b-closed set and soft multi β-closed set in soft topological spaces are defined.We show that every soft multi regular closed set is soft multi generalized regular closed set.

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