Notes on the spatial part of a frame | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 5، دوره 20، شماره 1، فروردین 2024، صفحه 105-129 اصل مقاله (600.72 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.48308/cgasa.2023.233584.1435 | ||
| نویسندگان | ||
| Igor Arrieta1؛ Jorge Picado* 2؛ Ales Pultr3 | ||
| 1School of Computer Science, University of Birmingham, B15 2TT Birmingham, UK | ||
| 2Department of Mathematics University of Coimbra PORTUGAL | ||
| 3Department of Applied Mathematics and ITI, MFF, Charles University, Malostranské ném. 24, 11800 Praha 1, Czech Republic | ||
| چکیده | ||
| A locale (frame) L has a largest spatial sublocale generated by the primes (spectrum points), the spatial part SpL. In this paper we discuss some of the properties of the embeddings SpL ⊆ L. First we analyze the behaviour of the spatial parts in the assembly: the points of L and of S(L)^op (∼= the congruence frame) are in a natural one-one correspondence while the topologies of SpL and Sp(S(L)^op) differ. Then we concentrate on some special types of embeddings of SpL into L, namely in the questions when SpL is complemented, closed, or open. While in the first part L was general, here we need some restrictions (weak separation axioms) to obtain suitable formulas | ||
| کلیدواژهها | ||
| Locale؛ prime element؛ spectrum؛ sublocale؛ supplement؛ Boolean sublocale؛ spatial part | ||
| مراجع | ||
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