Sets, complements and boundaries
نویسندگان
چکیده
The relations among a set, its complement, and its boundary are examined constructively. A crucial tool is a theorem that allows the construction of a point where a segment comes close to the boundary of a set in a Banach space. Brouwerian examples show that many of the results are the best possible.
منابع مشابه
Computably enumerable sets that are automorphic to low sets
We work with the structure consisting of all computably enumerable (c.e.) sets ordered by set inclusion. The question we will partially address is which c.e. sets are autormorphic to low (or low2) sets. Using work of R. Miller [9], we can see that every set with semilow complement is ∆3 automorphic to a low set. While it remains open whether every set with semilow complement is effectively auto...
متن کاملC0-coarse Geometry of Complements of Z-sets in the Hilbert Cube
Motivated by the Chapman Complement Theorem, we construct an isomorphism between the topological category of compact Z-sets in the Hilbert cube Q and the C0-coarse category of their complements. The C0coarse morphisms are, in this particular case, intrinsically related to uniformly continuous proper maps. Using that fact we are able to relate in a natural way some of the topological invariants ...
متن کاملPartial Differential Equations applied to Medical Image Segmentation
This paper presents an application of partial differential equations(PDEs) for the segmentation of abdominal and thoracic aortic in CTA datasets. An important challenge in reliably detecting aortic is the need to overcome problems associated with intensity inhomogeneities. Level sets are part of an important class of methods that utilize partial differential equations (PDEs) and have been exte...
متن کاملOn Complements of Sets and the Efremovic Condition in Pre-apartness Spaces
In this paper we study various properties of complements of sets and the Efremovič separation property in a symmetric pre–apartness space.
متن کاملThe Consistency of the Axiom of Choice and of the Generalized Continuum-Hypothesis.
1. The axiom of choice (i.e., v. Neumann's Ax. III 3*) 2. The generalized Continuum-Hypothesis (i.e., the statement that 2"= ,, + i holds for any ordinal a) 3. The existence of linear non-measurable sets such that both they and their complements are one-to-one projections of two-dimensional complements of analytic sets (and which therefore are B2-sets in Lusin's terminology2) 4. The existence o...
متن کامل