The search session has expired. Please query the service again.
The search session has expired. Please query the service again.
Displaying 1301 –
1320 of
8504
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...
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].
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...
Necessary conditions are found for a Cantor subset of the circle to be minimal for some -diffeomorphism. These conditions are not satisfied by the usual ternary Cantor set.
If a separable dense in itself metric space is not a union of countably many nowhere dense subsets, then its -space is not subsequential.
In a Tychonoff space , the point is called a -point if every real-valued continuous function on can be extended continuously to . Every point in an extremally disconnected space is a -point. A classic example is the space consisting of the countable ordinals together with . The point is known to be a -point as well as a -point. We supply a characterization of -points in totally ordered spaces. The remainder of our time is aimed at studying when a point in a product space is a -point....
Currently displaying 1301 –
1320 of
8504