2006•Mohu xitong yu shuxueRequires access

Two Important Properties of Cartesian Closed Domain Categories

Liu Ni

Abstract

For every Cartesian closed full subcategory [WTHT]C of CONT, the induced categories R-[WTHT]C (the category of all retracts of [WTHT]C-objects and Scott continuous) and B-[WTHT]C (the category of all bilimits of [WTHT]C-expanding-sequences and Scott continuous) are both proved to be Cartesian closed full subcategories of CONT. Since R-[WTHT]C and B-[WTHT]C both contain [WTHT]C as their full subcategory, a maximal Cartesian closed full subcategory of CONT must be closed with both retracts and bilimits of expanding- sequences. Also an equivalent statement of the famous open question in domain theory is given in terms of Cartesian closedness.

About this research paper

What this paper is about

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Key concepts: Subcategory, Cartesian closed category, Cartesian coordinate system, Mathematics, Domain (mathematical analysis), Pure mathematics, Statement (logic), Discrete mathematics