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 Open

Presents the pdf analysis as premium feature

PDF Analysis

Insights

Presents the summarisation as premium feature

Summarisation

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

<P>Part II of this study uses the path-following theory of labelled V-complexes developed in Part I to provide constructive algorithmic proofs of a variety of combinatorial lemmas in topology. We demonstrate two new dual lemmas on the n-dimensional cube, and use a generalized Sperner lemma to prove a generalization of the Knaster--Kuratowski--Mazurkiewicz covering lemma on the simplex. We also show that Tucker's lemma can be derived directly from the Borsuk--Ulam theorem. We report the interrelationships between these results, Brouwer's fixed point theorem, and the existence of stationary points on the simplex.</P>

Variable Dimension Complexes Part II: A Unified Approach to Some Combinatorial Lemmas in Topology