An Infinitary Version of Sperner's Lemma

نویسنده

  • Aarno Hohti
چکیده

We prove an extension of the well-known combinatorial-topological lemma of E. Sperner [20] to the case of infinite-dimensional cubes. It is obtained as a corollary to an infinitary extension of the Lebesgue Covering Dimension Theorem .

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A note on kernels and Sperner's Lemma

The kernel-solvability of perfect graphs was first proved by Boros and Gurvich, and later Aharoni andHolzmangave a shorter proof. Bothproofswere based on Scarf’s Lemma. In this note we show that a very simple proof can be given using a polyhedral version of Sperner’s Lemma. In addition, we extend the Boros–Gurvich theorem to h-perfect graphs and to a more general setting. © 2009 Elsevier B.V. A...

متن کامل

A Borsuk-Ulam Equivalent that Directly Implies Sperner's Lemma

We show that Fan’s 1952 lemma on labelled triangulations of the n-sphere with n + 1 labels is equivalent to the Borsuk–Ulam theorem. Moreover, unlike other Borsuk–Ulam equivalents, we show that this lemma directly implies Sperner’s Lemma, so this proof may be regarded as a combinatorial version of the fact that the Borsuk–Ulam theorem implies the Brouwer fixed-point theorem, or that the Lustern...

متن کامل

Fixed-Point Theorem, and Cohomology

1. INTRODUCTION. The proof of the Brouwer fixed-point Theorem based on Sperner's Lemma [S] is often presented as an elementary combi-natorial alternative to advanced proofs based on algebraic topology. See, for example, Section 6.3 of [P1]. One may ask if this proof is really based on ideas completely different from the ideas of algebraic topology (and, in particular, the ideas of Brouwer's own...

متن کامل

On Total Functions, Existence Theorems and Computational Complexity

Megiddo, N. and C.H. Papadimitriou, On total functions, existence theorems and computational complexity (Note), Theoretical Computer Science 81 (1991) 317-324. wondeterministic multivalued functions with values that are polynomially verifiable and guaranteed to exist form an interesting complexity class between P and NP. We show that this class, which we call TFNP, contains a host of important ...

متن کامل

Deducing the Multidimensional Szemerédi Theorem from the Infinitary Hypergraph Removal Lemma

We offer a new proof of the Furstenberg-Katznelson multiple recurrence theorem for several commuting probability-preserving transformations T1, T2, . . . , Td : Z y (X,Σ, μ) ([5]), and so, via the Furstenberg correspondence principle introduced in [4], a new proof of the multi-dimensional Szemerédi Theorem. We bypass the detailed analysis of certain towers of factors of a probability-preserving...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2002