Idempotent probability measures spaces on П-complete spaces and maps
Idempotent probability measures spaces on П-complete spaces and maps
DOI:
https://doi.org/10.56143/ujmcs.v1i2.12/Keywords:
идемпотентные вероятностные меры, конечный носитель, пространства идемпотентных вероятностных мер, индуцированные отображения, звёздно-конечное открытое покрытие, конечно-компонентное покрытие, совершенная компактификация, компактификация Стоуна--Чexа.Abstract
In this paper we study the behavior of П-completeness for Tychonoff maps under the functor of idempotent probability measures with finite support. We prove that a Tychonoff map is П-complete if and only if the induced map between the corresponding spaces of idempotent probability measures is П-complete. As a consequence, the functor of idempotent probability measures with finite support both preserves and reflects П-completeness for maps. This provides a convenient criterion for verifying П-completeness via induced mappings and supports the transfer of completeness-type properties to functorially constructed spaces. The obtained result yields a lifting of the functor to the category whose objects are П-complete spaces and whose morphisms are П-complete maps.
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