scholarly journals A note on finite codimensional linear isometries ofC(X)intoC(Y)

1995 ◽  
Vol 18 (4) ◽  
pp. 677-680 ◽  
Author(s):  
Sin-Ei Takahasi ◽  
Takateru Okayasu
Keyword(s):  
Finite Codimension ◽  
Hausdorff Spaces ◽  
Linear Isometry ◽  
Continuous Maps ◽  
Linear Isometries

Let(X,Y)be a pair of compact Hausdorff spaces. It is shown that a certain property of the class of continuous maps ofYontoXis equivalent to the non-existence of linear isometry ofC(X)intoC(Y)whose range has finite codimension>0.

Real-linear isometries between certain subspaces of continuous functions

2013 ◽  
Vol 11 (11) ◽  
Author(s):  
Arya Jamshidi ◽  
Fereshteh Sady
Keyword(s):  
Metric Spaces ◽  
Continuous Functions ◽  
Supremum Norm ◽  
Hausdorff Spaces ◽  
Linear Isometry ◽  
Compact Metric Spaces ◽  
Separating Property ◽  
Similar Description ◽  
Real Linear ◽  
Linear Isometries

AbstractIn this paper we first consider a real-linear isometry T from a certain subspace A of C(X) (endowed with supremum norm) into C(Y) where X and Y are compact Hausdorff spaces and give a result concerning the description of T whenever A is a uniform algebra on X. The result is improved for the case where T(A) is, in addition, a complex subspace of C(Y). We also give a similar description for the case where A is a function space on X and the range of T is a real subspace of C(Y) satisfying a ceratin separating property. Next similar results are obtained for real-linear isometries between spaces of Lipschitz functions on compact metric spaces endowed with a certain complete norm.

Projective Elements in Categories with Perfect θ-Continuous Maps

1981 ◽  
Vol 33 (4) ◽  
pp. 872-884 ◽  
Author(s):  
Hans Vermeer ◽  
Evert Wattel
Keyword(s):  
Hausdorff Space ◽  
Continuous Functions ◽  
List Type ◽  
Hausdorff Spaces ◽  
Extremally Disconnected ◽  
Continuous Maps

In 1958 Gleason [6] proved the following :THEOREM. In the category of compact Hausdorff spaces and continuous maps, the projective elements are precisely the extremally disconnected spaces.The projective elements in many topological categories with perfect continuous functions as morphisms have been found since that time. For example: In the following categories the projective elements are precisely the extremally disconnected spaces:(i) The category of Tychonov spaces and perfect continuous functions. [4] [11].(ii) The category of regular spaces and perfect continuous functions. [4] [12].(iii) The category of Hausdorff spaces and perfect continuous functions. [10] [1].(iv) In the category of Hausdorff spaces and continuous k-maps the projective members are precisely the extremally disconnected k-spaces. [14].In 1963 Iliadis [7] constructed for every Hausdorff space X the so called Iliadis absolute E[X], which is a maximal pre-image of X under irreducible θ-continuous maps.

scholarly journals Projective bitopological spaces II.

1972 ◽  
Vol 14 (1) ◽  
pp. 119-128 ◽  
Author(s):  
M. C. Datta
Keyword(s):  
Full Subcategory ◽  
Hausdorff Spaces ◽  
Extremally Disconnected ◽  
Continuous Maps ◽  
Bitopological Spaces ◽  
Perfect Maps

Gleason [3] proved that in the category G of compact Hausdorff spaces and continuous maps, the projective objects are precisely the extremally disconnected spaces contained in the category. Strauss [7] generalised this and proved that in the category G of regular Hausdorif spaces and perfect maps the projective objects are again precisely the extremally disconnected ones. Observe that Gleason's category is a full subcategory of Strauss's category.

scholarly journals On dimension andweight of a local contact algebra

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5481-5500
Author(s):  
G. Dimov ◽  
E. Ivanova-Dimova ◽  
I. Düntsch
Keyword(s):  
Compact Hausdorff Space ◽  
Hausdorff Space ◽  
Hausdorff Spaces ◽  
Locally Compact ◽  
Local Contact ◽  
Continuous Maps ◽  
Contact Algebra ◽  
Contact Algebras ◽  
Locally Compact Hausdorff Space

As proved in [16], there exists a duality ?t between the category HLC of locally compact Hausdorff spaces and continuous maps, and the category DHLC of complete local contact algebras and appropriate morphisms between them. In this paper, we introduce the notions of weight wa and of dimension dima of a local contact algebra, and we prove that if X is a locally compact Hausdorff space then w(X) = wa(?t(X)), and if, in addition, X is normal, then dim(X) = dima(?t(X)).

scholarly journals A functor IS in the Category Compact Hausdorff Spaces

2020 ◽  
Vol 6 (3) ◽  
pp. 13-22
Author(s):  
Kh. Kurbanov ◽  
S. Yodgarov
Keyword(s):  
Hausdorff Spaces ◽  
Normal Functor ◽  
Compact Spaces ◽  
Continuous Maps

We construct a space of normed, homogeneous and max-plus-semiadditive functionals and we give its description. Further we establish that the construction of taking of a space of normed, homogeneous and max-plus-semiadditive functionals, forms a normal functor acting in the category of Hausdorff compact spaces and their continuous maps.

More on Compact Hausdorff Spaces and Finitary Duality

1984 ◽  
Vol 36 (6) ◽  
pp. 1113-1118 ◽  
Author(s):  
B. Banaschewski
Keyword(s):  
Hausdorff Spaces ◽  
Cartesian Products ◽  
First Order ◽  
Continuous Maps ◽  
Dual Equivalence

It is an old conjecture by P. Bankston that the category CompHaus of compact Hausdorff spaces and their continuous maps is not dually equivalent to any elementary P-class of finitary algebras (taken as a category with all homomorphisms between its members as maps), where elementary means defined by first order axioms, and a P-class is one closed under arbitrary (cartesian) products. One motivation for this conjecture is the fact that such a dual equivalence would make ultracopowers of compact Hausdorff spaces correspond to ultrapowers of finitary algebras, and one might expect this to have contradictory consequences.As a possible step towards proving his conjecture, Bankston [2] showed that no elementary SP-class of finitary algebras can be dually equivalent to CompHaus. However, it was subsequently proved in [1] that the same holds for any SP-class of finitary algebras, using an argument independent of ultrapowers.

On hull classes of ℓ-groups and covering classes of spaces

2011 ◽  
Vol 61 (3) ◽  
Author(s):  
Ricardo Carrera ◽  
Anthony Hager
Keyword(s):  
Hausdorff Spaces ◽  
Central Idea ◽  
Weak Unit ◽  
Hull Class ◽  
Continuous Maps ◽  
The Relationship

AbstractW denotes the category of archimedean ℓ-groups with designated weak unit and ℓ-homomorphisms that preserve the weak unit. Comp denotes the category of compact Hausdorff spaces with continuous maps. The Yosida functor is used to investigate the relationship between hull classes in W and covering classes in Comp. The central idea is that of a hull class whose hull operator preserves boundedness. We demonstrate how the Yosida functor may be used to identify hull classes in W and covering classes in Comp. In addition, we exhibit an array of order preserving bijections between certain families of hull classes and all covering classes, one of which was recently produced by Martínez. Lastly, we apply our results to answer a question of Knox and McGovern about the class of all feebly projectable ℓ-groups.

scholarly journals Linear Isometries between Real Banach Algebras of Continuous Complex-Valued Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Davood Alimohammadi ◽  
Hadis Pazandeh
Keyword(s):  
Composition Operators ◽  
Banach Algebras ◽  
Extreme Points ◽  
Function Algebra ◽  
Hausdorff Spaces ◽  
Uniform Function ◽  
Weighted Composition ◽  
Continuous Complex ◽  
Complex Valued ◽  
Linear Isometries

Let and be compact Hausdorff spaces, and let and be topological involutions on and , respectively. In 1991, Kulkarni and Arundhathi characterized linear isometries from a real uniform function algebra on (, ) onto a real uniform function algebra on (, ) applying their Choquet boundaries and showed that these mappings are weighted composition operators. In this paper, we characterize all onto linear isometries and certain into linear isometries between and applying the extreme points in the unit balls of and .

Extensive Subcategories in Universal Topological Algebras

1977 ◽  
Vol 29 (1) ◽  
pp. 71-76
Author(s):  
T. H. Choe ◽  
Y. H. Hong
Keyword(s):  
Topological Spaces ◽  
Topological Algebras ◽  
Hausdorff Spaces ◽  
Limit Operators ◽  
Coreflective Subcategory ◽  
Continuous Maps

Herrlich [7] has introduced the limit-operators to obtain every coreflective subcategory of the category Top of topological spaces and continuous maps. Using limit-operators, S. S. Hong [9] has constructed new reflective subcategories from a known extensive subcategory of a hereditary category of Hausdorff spaces and continuous maps.

Extensive Subcategories of the Category of T1-spaces

1975 ◽  
Vol 27 (2) ◽  
pp. 311-318 ◽  
Author(s):  
Sung Sa Hong
Keyword(s):  
Topological Spaces ◽  
Hausdorff Spaces ◽  
Reflective Subcategory ◽  
Continuous Maps

It is well known that epimorphisms in the category Top (Top1, respectively) of topological spaces (T1spaces, respectively) and continuous maps are precisely onto continuous maps. Since every mono-reflective subcategory of a category is also epi-reflective and every embedding in Top (Top1, respectively) is a monomorphism, there is no nontrivial reflective subcategory of Top (Top1 respectively) such that every reflection is an embedding. However, in the category Top0 of T0-spaces and continuous maps as well as in the category Haus of Hausdorff spaces and continuous maps, there are epimorphisms which are not onto. Moreover, every reflection of a reflective subcategory of Top0, which contains a non T1-space, is an embedding [16].

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