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Displaying 1301 – 1320 of 8506

Brouwer Fixed Point Theorem for Simplexes

Karol Pąk (2011)

Formalized Mathematics

In this article we prove the Brouwer fixed point theorem for an arbitrary simplex which is the convex hull of its n + 1 affinely indepedent vertices of εn. First we introduce the Lebesgue number, which for an arbitrary open cover of a compact metric space M is a positive real number so that any ball of about such radius must be completely contained in a member of the cover. Then we introduce the notion of a bounded simplicial complex and the diameter of a bounded simplicial complex. We also prove...

Brouwer Fixed Point Theorem in the General Case

Karol Pąk (2011)

Formalized Mathematics

In this article we prove the Brouwer fixed point theorem for an arbitrary convex compact subset of εn with a non empty interior. This article is based on [15].

Brouwer Invariance of Domain Theorem

Karol Pąk (2014)

Formalized Mathematics

In this article we focus on a special case of the Brouwer invariance of domain theorem. Let us A, B be a subsets of εn, and f : A → B be a homeomorphic. We prove that, if A is closed then f transform the boundary of A to the boundary of B; and if B is closed then f transform the interior of A to the interior of B. These two cases are sufficient to prove the topological invariance of dimension, which is used to prove basic properties of the n-dimensional manifolds, and also to prove basic properties...

Browder-Fan fixed point theorem and related results

Paul Deguire (1995)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

Browder's fixed point theorem and some interesting results in intuitionistic fuzzy normed spaces.

Cancan, M. (2010)

Fixed Point Theory and Applications [electronic only]

Browder's type strong convergence theorems for infinite families of nonexpansive mappings in Banach spaces.

Suzuki, Tomonari (2006)

Fixed Point Theory and Applications [electronic only]

Buchwalter-Schmets theorems and linear topologies.

Sánchez Ruiz, L.M., Ferrer, J.R. (1999)

International Journal of Mathematics and Mathematical Sciences

Building closed categories

Michael Barr (1978)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

$C_{0}$ -biČech spaces and $C_{1}$ -biČech spaces.

Boonpok, Chawalit (2009)

Acta Mathematica Academiae Paedagogicae Nyí regyháziensis. New Series [electronic only]

$C_{0}$ -spaces and $C_{1}$ -spaces.

Boonpok, Chawalit (2009)

Acta Universitatis Apulensis. Mathematics - Informatics

$C^{1}$ -minimal subsets of the circle

Dusa McDuff (1981)

Annales de l'institut Fourier

Necessary conditions are found for a Cantor subset of the circle to be minimal for some $C^{1}$ -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.

$C^{1}$ weakly chaotic functions with zero topological entropy and non- flat critical points.

Jiménez López, Víctor (1991)

Acta Mathematica Universitatis Comenianae. New Series

C- and C*-quotients in pointfree topology [Book]

Richard N. Ball, Joanne Walters-Wayland (2002)

$C$ -compactness modulo an ideal.

Gupta, M.K., Noiri, T. (2006)

International Journal of Mathematics and Mathematical Sciences

$c$ -continuity and closed graphs

Tibor Neubrunn (1985)

Časopis pro pěstování matematiky

$C_{p} (I)$ is not subsequential

Viacheslav I. Malykhin (1999)

Commentationes Mathematicae Universitatis Carolinae

If a separable dense in itself metric space is not a union of countably many nowhere dense subsets, then its $C_{p}$ -space is not subsequential.

$C_{p}$ -Movably regular convergences

Zvonko Čerin (1983)

Fundamenta Mathematicae

$C^{*}$ -points vs $P$ -points and $P^{♭}$ -points

Jorge Martinez, Warren Wm. McGovern (2022)

Commentationes Mathematicae Universitatis Carolinae

In a Tychonoff space $X$ , the point $p \in X$ is called a $C^{*}$ -point if every real-valued continuous function on $C ∖ {p}$ can be extended continuously to $p$ . Every point in an extremally disconnected space is a $C^{*}$ -point. A classic example is the space $𝐖^{*} = ω_{1} + 1$ consisting of the countable ordinals together with $ω_{1}$ . The point $ω_{1}$ is known to be a $C^{*}$ -point as well as a $P$ -point. We supply a characterization of $C^{*}$ -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space is a $C^{*}$ -point....

$C_{q}$ -commuting maps and invariant approximations.

Hussain, N., Rhoades, B.E. (2006)

Fixed Point Theory and Applications [electronic only]

$C$ -spaces and simplicial complexes.

Fedorchuk, V.V. (2009)

Sibirskij Matematicheskij Zhurnal

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