Results 41 to 50 of about 141 (99)

Joins of Closed Sublocales are not Always A Coframe

Order
Abstract Given a locale L , the ordered collection $$\textsf{S}_c(L)$$ S
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Ideals of function rings associated with sublocales

, 2021
The ring of real-valued continuous functions on a completely regular frame L is denoted by RL. As usual, βL denotes the Stone-Cech compactification of ˇ L. In the thesis we study ideals of RL induced by sublocales of βL. We revisit the notion of purity
Stephen, Dorca Nyamusi
core  

Unsurprising results on localic groups

, 1990
If A and B are subsets of a topological group, one of which is open, then AB is open. A ‘pointless’ proof of the corresponding result for localic groups is given. A fundamental tool is Lemma 2 in this paper, which states that if S and T are sublocales of
Wraith, G.C.
core   +1 more source

Revisiting the relation between subspaces and sublocales

, 2020
We revisit results concerning the connection between subspaces of a space and sublocales of its locale of open sets. The approach we present is based on the observation that for every locale $L$ its spatial sublocales $\mathsf{sp}[\mathsf{S}(L)]$ form a coframe which is isomorphic to the coframe $\mathsf{sob}[\mathcal{P}(\mathsf{pt}(L))]$ of sober ...
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Lindelöf tightness and the Dedekind-MacNeille completion of a regular σ-frame

, 2017
Tightness is a notion that arose in an attempt to understand the reverse reflection problem: given a monoreflection of a category onto a subcategory, determine which sub-objects of an object in the subcategory reflect to it - those which do are termed ...
Pultr, A, Ball, R.N., Moshier, M.A., Walters-Wayland, J.L.   +3 more
core  

On relatively connected sublocales and \(J\)-frames

Categories and General Algebraic Structures with Applications
Summary: In this paper, we present a study of relatively connected sublocales. Connected sublocales are relatively connected, not conversely. We study conditions under which relatively connected sublocales are connected. The development of this study is subsequently utilized to characterize what we call \(C\)-normal frames.
Simo Mthethwa, Siyabonga Dubazana
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A Verified Implementation of the Berlekamp-Zassenhaus Factorization Algorithm. [PDF]

J Autom Reason, 2020
Divasón J, Joosten SJC, Thiemann R, Yamada A.   +3 more
europepmc   +1 more source

Remoteness in the category of bilocales

In locale theory, a sublocale is said to be remote in case it misses every nowhere dense sublocale. In this paper, we introduce and study a new class of sublocales in the category of bilocales, namely (i,j)-remote sublocales.
Nxumalo, Mbekezeli
core  

The clean elements of the ring $\mathcal R(L)$

summary:We characterize clean elements of $\mathcal R(L)$ and show that $\alpha \in \mathcal {R}(L)$ is clean if and only if there exists a clopen sublocale $U$ in $L$ such that $\frak {c}_L({\rm coz} (\alpha - {\bf 1})) \subseteq U \subseteq \frak {o}_L(
Taha, Maryam, Estaji, Ali Akbar
core   +1 more source

Joins of closed sublocales

, 2019
Sublocales that are joins of closed ones constitute a frame S_Vc(L) embedded as a sup-sublattice into the coframe S(L) of sublocales of L. We prove that in the case of subfit L it is a subcolocale of S(L), that it is then a Boolean algebra and in fact precisely the Booleanization of S(L).
Picado, Jorge, Pultr, Aleš, Tozzi, Anna
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