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On the largest coreflective Cartesian closed subconstruct of Prtop

1996
*
Applied Categorical Structures
*

This implies that

doi:10.1007/bf00124115
fatcat:nrhitewlovcgdady2wuxxg3soy
*in*any coreflective subconstruct*of**Prtop*,*exponential*objects are finitely generated. ... Moreover,*in*any finitely productive, coreflective subconstruct,*exponential*objects are precisely those objects*of*the subconstruct that are finitely generated. ... Since we work only with well-fibred topological constructs C, we use the following*characterization**of*an*exponential*object: X is*exponential**in*C if and only if the functor X × -preserves final epi-sinks ...##
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On the Largest Coreflective Cartesian Closed Subconstruct of Prtop
[chapter]

1996
*
Categorical Topology
*

This implies that

doi:10.1007/978-94-009-0263-3_6
fatcat:wrrm6gpssbdyrcplweifgulcom
*in*any coreflective subconstruct*of**Prtop*,*exponential*objects are finitely generated. ... Moreover,*in*any finitely productive, coreflective subconstruct,*exponential*objects are precisely those objects*of*the subconstruct that are finitely generated. ... Since we work only with well-fibred topological constructs C, we use the following*characterization**of*an*exponential*object: X is*exponential**in*C if and only if the functor X × -preserves final epi-sinks ...##
###
Exponential objects and Cartesian closedness in the constructPrtop

1993
*
Applied Categorical Structures
*

We give an internal

doi:10.1007/bf00872940
fatcat:a4hcthtsabcntfdjzzbojdxptq
*characterization**of*the*exponential*objects*in*the construct*Prtop*and investigate Cartesian closedness for coreflective or topological full subconstructs*of**Prtop*. ... With regard to topological full subconstructs*of**Prtop*we give an example*of**a*Cartesian closed one that is large enough to contain all topological Frtchet spaces and all TI pretopological Frtchet spaces ... This result disproves the conjecture formulated*in*[16] that the*exponential*objects*in**Prtop*can be*characterized*by some filter-theoretic description*of*core-compactness. ...##
###
Classes of pretopological spaces closed under the formation of final structures

1996
*
Topology and its Applications
*

We investigate coreflective subconstructs

doi:10.1016/0166-8641(95)00097-6
fatcat:tfcpep7kkfavjj4gmmw6pha2sa
*of*the construct h-top*of*pretopological spaces and continuous*maps*and*in*particular the inclusion "order" between these subconstructs. ... Using these minimal elements we obtain*a*"partition"*of*the whole conglomerate*of*coreflective subconstructs*of*&top. ...*In*the topological construct*Prtop**of*pretopological spaces and continuous*maps*final structures are formed*in**a*very easy and elegant way. Moreover quotients*in**Prtop*are hereditary [3, 12] . ...##
###
Page 7272 of Mathematical Reviews Vol. , Issue 94m
[page]

1994
*
Mathematical Reviews
*

Summary: “We give an internal

*characterization**of*the*exponential*objects*in*the construct*Prtop*and investigate Cartesian closedness for co-reflective or topological full subconstructs*of**Prtop*. ... (B-VUB; Brussels)*Exponential*objects and Cartesian closedness*in*the construct*Prtop*. (English summary) Appl. Categ. Structures 1 (1993), no. 4, 345-360. ...##
###
Page 1746 of Mathematical Reviews Vol. , Issue 97C
[page]

1997
*
Mathematical Reviews
*

Summary: “We give

*characterizations**of*perfect*maps*(as well as*of*continuous*maps*and compact*maps*)*in*metric spaces*in*terms ... This implies that*in*any coreflective subconstruct*of**Prtop*,*exponential*ob- jects are finitely generated. ...##
###
Injective Convergence Spaces and Equilogical Spaces via Pretopological Spaces

2006
*
Electronical Notes in Theoretical Computer Science
*

On the other hand, we study the category

doi:10.1016/j.entcs.2005.11.065
fatcat:q2entdrus5ccvkgethlw5ccqea
*PrTop**of*pretopological spaces that lies*in*-between Top and Conv/Equ, identify its injective spaces, and show that they are also injective*in*Conv and Equ. ... Sierpinski space Ω is injective*in*the category Top*of*topological spaces, but not*in*any*of*the larger cartesian closed categories Conv*of*convergence spaces and Equ*of*equilogical spaces. ... Such*a**characterization*is also possible*in*case*of**PrTop*, but is actually much simpler. ...##
###
Exponentiation for unitary structures

2006
*
Topology and its Applications
*

For T = U the ultrafilter monad, we

doi:10.1016/j.topol.2005.01.037
fatcat:zjjxs34vdfbepjiln4oxjt5s44
*characterize**exponentiable*morphisms*in*Alg u (U; V). ... Further, we give*a*sufficient condition for an object to be*exponentiable**in*the category Alg(U; V)*of*reflexive and transitive lax algebras. ... Our result covers the*characterization**of**exponentiable*morphisms*in**PrTop*obtained*in*[24] ,*of**exponentiable*objects*in*PrAp obtained*in*[20] , and it gives*a*new*characterization**of**exponentiable*...##
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Topological improvements of categories of structured sets

1987
*
Topology and its Applications
*

Hulls

doi:10.1016/0166-8641(87)90101-5
fatcat:swfvqfnmabcmrgftsncjclvzhu
*In*this section various extensions*of**a*construct*A*, i.e., full concrete embeddings E :*A*+ P(*A*) are*characterized*. ...*Of*the familiar topological constructs, listed*in*1.1, only*PrTop*, PsTop, Conv, Mer, Bor, Simp and Rere are hereditary. ... Reiterman, The quasitopos hull*of*the category*of*uniform spaces, Topology Appl. 27 (1987) ...##
###
Page 3677 of Mathematical Reviews Vol. , Issue 2004e
[page]

2004
*
Mathematical Reviews
*

However it is shown that the three generalized functors are equiv- alent.”
2004e:18005 18B30 18A20 54B30 54C10
Richter, Giinther (D-BLFM; Bielefeld)

*A**characterization**of**exponentiable**maps**in**PrTop*. ... Surprisingly or not, it turns out to*characterize**exponentiable**maps*.” ...##
###
Initially dense objects for metrically generated theories

2009
*
Topology and its Applications
*

*a*r t i c l e i n f o

*a*b s t r

*a*c t MSC: 54B30 54A05 18B99 We study initially dense objects for metrically generated constructs X

*in*the sense

*of*[E. Colebunders, R. ... For the base categories consisting

*of*metrics, quasi-metrics, totally bounded quasi-metrics and totally bounded metrics,

*a*general description

*of*some initially dense objects is given

*in*case the expander ... Acknowledgement I thank Eva Vandersmissen for her valuable comments towards some examples which appear

*in*this paper. ...

##
###
The quasitopos hull of the construct of closure spaces

2003
*
Applied General Topology
*

The topological construct Cls

doi:10.4995/agt.2003.2006
fatcat:7lzxrebm2jf4zdhneucut2fgl4
*of*closure spaces and continuous*maps*is not*a*quasitopos.*In*this article we give an explicit description*of*the quasitopos topological hull*of*Cls using*a*method*of*F. ... <p>*In*the list*of*convenience properties for topological constructs the property*of*being*a*quasitopos is one*of*the most interesting ones for investigations*in*function spaces, differential calculus, ...*In**a*well-fibred topological construct D, this notion can be*characterized*as follows: X is*exponential**in*D iff for each D-object Y the set Hom D (X, Y ) can be supplied with the structure*of**a*D-object ...##
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Page 1474 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

(English summary) 2003d:18002
— Non-symmetric

*exponential*laws*in*the construct*PrTop*. (English summary) 2003f: 18008 Slapal, Josef Compactness with respect to*a*convergence structure. ... On t-pseudocompact*mappings*. (Russian. Russian summary) 20034:54023 Nordo, Giorgio (with Pasynkov, Boris*A*.)*Characterizing*continuity*in*topological spaces. ...##
###
Page 317 of Mathematical Reviews Vol. 25, Issue Index
[page]

*
Mathematical Reviews
*

(English summary) [Euler-Jordan and Gauss functions and

*exponential**in*Burnside semirings}] 93f:18008 Kennison, John F. ... ., 93f:18007 Vazquez, Roberto Simple objects*in*categories. (Spanish) 93h:18007 Wang, Hao? (with Hu, Qing Ping) Four types*of*morphism-*map*categories and their properties. (Chinese. ...##
###
Page 2094 of Mathematical Reviews Vol. , Issue Index
[page]

*
Mathematical Reviews
*

No. 150 (2003), 338-342. 81Q50 (81-05)
Richter, Giinther'

*A**characterization**of**exponentiable**maps**in**PrTop*. (English summary) Appl. Categ. Structures 11 (2003), no. 3, 261-265. ... (Summary) 2004e:18005 18B30 (18A20, 54B30, 54C10) —*Exponentiability*for*maps*means fibrewise core-compactness. (English summary) J. Pure Appl. Algebra 187 (2004), no. 1-3, 295-303. (D. ...
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