$L$-enriched topological systems---a common framework of $L$-topology and $L$-frames

author

  • M. Liu School of Sciences, Chang'an University, Xi'an, China
Abstract:

Employing the notions of the strong $L$-topology introduced by Zhangand the $L$-frame introduced by Yao  and the concept of $L$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf St$L$-Top} of strong$L$-topological spaces, {bf S$L$-Loc} of strict $L$-locales and{bf $L$-EnTopSys} of $L$-enriched topological systems. All of theseconcepts are essentially based on the theory of $L$-enrichedcategories, thus we obtain a unified enriched-categorical version ofthe classical adjunctions among the categories {bf Top} oftopological spaces, {bf Loc} of locales and {bf TopSys} oftopological systems, as well as a unified enriched-categoricalapproach to treating these concepts.

Upgrade to premium to download articles

Sign up to access the full text

Already have an account?login

similar resources

$l$-enriched topological systems---a common framework of $l$-topology and $l$-frames

employing the notions of the strong $l$-topology introduced by zhangand the $l$-frame introduced by yao  and the concept of $l$-enrichedtopological system defined in the present paper, we constructadjunctions among the categories {bf st$l$-top} of strong$l$-topological spaces, {bf s$l$-loc} of strict $l$-locales and{bf $l$-entopsys} of $l$-enriched topological systems. all of theseconcepts are ...

full text

A note on specialization L-preorder of L-topological spaces, L-fuzzifying topological spaces, and L-fuzzy topological spaces

It is shown that, for any spatial frame L (i.e., L is a complete lattice generated by the set of all prime elements), both the specialization L-preorder of L-topological spaces introduced by Lai and Zhang [Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems 157 (2006) 1865–1885] and that of L-fuzzifying topological spaces introduced by Fang and Qiu [Fuzzy orders and fuzzifying topologies,...

full text

Various L-signatures and a topological L-signature theorem

For a normal covering over a closed oriented topological manifold we give a proof of the L-signature theorem with twisted coefficients, using Lipschitz structures and the Lipschitz signature operator introduced by Teleman. We also prove that the L-theory isomorphism conjecture as well as the C∗ max-version of the Baum-Connes conjecture imply the L-signature theorem for a normal covering over a ...

full text

L-Py, an open L-systems framework in Python

L-systems were conceived as a mathematical framework for modeling growth of plants. In this paper, we present L-Py, a simulation software that mixes L-systems construction with the Python high-level modeling language. In addition to this software module, an integrated visual development environment has been developed that facilitates the creation of plant models. In particular, easy to use opti...

full text

L – A Common Lisp for Embedded Systems

A commercially available system has been developed which allows for the use of Common Lisp in real time embedded control systems. The backbone of this system is a language called L. L is a subset of Common Lisp with multi-processing extensions. It is ideal for use in embedded systems with small computers. The system has a minimal memory footprint and can run on small processors. L contains both...

full text

Extension of shift-invariant systems in L(R) to frames

In this paper we show that any shift-invariant Bessel sequence with an at most countable number of generators can be extended to a tight frame for its closed linear span by adding another shift-invariant system with at most the same number of generators. We show that in general this result is optimal, by providing examples where it is impossible to obtain a tight frame by adding a smaller numbe...

full text

My Resources

Save resource for easier access later

Save to my library Already added to my library

{@ msg_add @}


Journal title

volume 11  issue 5

pages  93- 103

publication date 2014-10-30

By following a journal you will be notified via email when a new issue of this journal is published.

Hosted on Doprax cloud platform doprax.com

copyright © 2015-2023