Exponential objects and Cartesian closedness in the constructPrtop

1993 ◽  
Vol 1 (4) ◽  
pp. 345-360 ◽  
Author(s):  
E. Lowen-Colebunders ◽  
G. Sonck
Keyword(s):  
Cartesian Closedness

scholarly journals Cartesian-closedness and Subcategories of (L,M)-fuzzy Q-convergence Spaces

2021 ◽  
Author(s):  
Bin Pang ◽  
Lin Zhang
Keyword(s):  
Function Space ◽  
Convergence Spaces ◽  
Cartesian Closedness

Abstract In this paper, we first construct the function space of ( L,M )-fuzzy Q-convergence spaces to show the Cartesian-closedness of the category ( L,M )- QC of ( L,M )-fuzzy Q-convergence spaces. Secondly, we introduce several subcategories of ( L,M )- QC , including the category ( L,M )- KQC of ( L,M )-fuzzy Kent Q-convergence spaces, the category ( L,M )- LQC of ( L,M )-fuzzy Q-limit spaces and the category ( L,M )- PQC of ( L,M )-fuzzy pretopological Q-convergence spaces, and investigate their relationships.

scholarly journals The category of uniform convergence spaces is cartesian closed

1976 ◽  
Vol 15 (3) ◽  
pp. 461-465 ◽  
Author(s):  
R.S. Lee
Keyword(s):  
Uniform Convergence ◽  
Function Spaces ◽  
Convergence Spaces ◽  
Cartesian Closedness ◽  
Cartesian Closed ◽  
And Function

This paper first assigns specific uniform convergence structures to the products and function spaces of pairs of uniform convergence spaces, and then establishes a bijection between corresponding sets of morphisms which yields cartesian closedness.

scholarly journals Partiality, cartesian closedness, and toposes

1989 ◽  
Vol 80 (1) ◽  
pp. 50-95 ◽  
Author(s):  
P.-L. Curien ◽  
A. Obtułowicz
Keyword(s):  
Cartesian Closedness

Initially Structured Categories and Cartesian Closedness

1975 ◽  
Vol 27 (6) ◽  
pp. 1361-1377 ◽  
Author(s):  
L. D. Nel
Keyword(s):  
Topological Category ◽  
Separation Axiom ◽  
Striking Result ◽  
Cartesian Closedness ◽  
Special Cases ◽  
Selection Of

In recent papers Horst Herrlich [4; 5] has demonstrated the usefulness of topological categories for applications to a large variety of special structures. A particularly striking result is his characterization of cartesian closedness for topological categories (see [5]). Spaces satisfying a separation axiom usually cannot form a topological category in Herrlich's sense however and some interesting special cases, e.g. Hausdorff C-spaces, remain excluded from his theory despite having many analogous properties. It therefore seems worthwhile to undertake a similar study in a wider setting. To this end we relax one of the axioms for a topological category and show that in the resulting initially structured categories a significant selection of results can still be proved, including the characterization of cartesian closedness.

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