McKinsey-Tarski algebras and Raney extensions

2025/09/01 by Guram Bezhanishvili, Bezhanishvili, Guram, Ranjitha Raviprakash +5 · 1 citation
Mathematics · #06D22 #06E25 #18F60 #18F70 #54D10 #54E05 #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2509.01233

openalex publication_date 2025/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We introduce the notion of Raney morphism between MT-algebras and show that the resulting category is equivalent to the category of Raney extensions. This is done by generalizing the construction of the Funayama envelope of a frame. The resulting notion of the T₀-hull of a Raney extension generalizes that of the T_D-hull of a frame.

Citations

• Local compactness does not always imply spatiality
• The Funayama envelope as the T_D-hull of a frame
• McKinsey-Tarski Algebras: An alternative pointfree approach to topology

Cited by

• Strictly zero-dimensional biframes and Raney extensions

Related

• The Funayama envelope as the T_D-hull of a frame
• Raney extensions of frames: topological aspects
• McKinsey-Tarski Algebras: An alternative pointfree approach to topology
• Raney extensions: a pointfree theory of T₀ spaces based on canonical extension
• Strictly zero-dimensional biframes and Raney extensions