Sheaves and \(\mathfrak{T}a\)-bicompactifications of mappings. (English) Zbl 1132.54316

Summary: We study relations between bicompactifications of mappings and sheaves of algebras. Bicompactifications of mappings are a generalization of compactifications of topological spaces, and sheaves of algebras take place of algebras of continuous bounded functions on topological spaces. The main result reads as follows: there exists a one-to-one correspondence preserving the order between the set of all \(\mathfrak{T}a\)-bicompactifications of a given mapping and the set of all sheaves of a special kind.


54C25 Embedding
54C10 Special maps on topological spaces (open, closed, perfect, etc.)
54C35 Function spaces in general topology
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