English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

Convex sets appear in various mathematical theories, and are used to definenotions such as convex functions and hulls. As an abstraction from the usualdefinition of convex sets in vector spaces, we formalize in Coq an intrinsicaxiomatization of convex sets, namely convex spaces, based on an operationtaking barycenters of points. A convex space corresponds to a specific typethat does not refer to a surrounding vector space. This simplifies thedefinitions of functions on it. We show applications including the convexity ofinformation-theoretic functions defined over types of distributions. We alsoshow how convex spaces are embedded in conical spaces, which are abstract realcones, and use the embedding as an effective device to ease calculations.

Formal Adventures in Convex and Conical Spaces