Remainders of arcwise connected compactifications of the plane
نویسندگان
چکیده
منابع مشابه
On Compactifications with Path Connected Remainders
We prove that every separable and metrizable space admits a metrizable compactification with a remainder that is both path connected and locally path connected. This result answers a question of P. Simon. Connectedness and compactness are two fundamental topological properties. A natural question is whether a given space admits a connected (Hausdorff) compactification. This question has been st...
متن کاملAbout remainders in compactifications of paratopological groups
In this paper, we prove a dichotomy theorem for remainders in compactifications of paratopological groups: every remainder of a paratopological group $G$ is either Lindel"{o}f and meager or Baire. Furthermore, we give a negative answer to a question posed in [D. Basile and A. Bella, About remainders in compactifications of homogeneous spaces, Comment. Math. Univ. Caroli...
متن کاملColouring Arcwise Connected Sets in the Plane II
Let G be the family of nite collections S where S is a collection of closed, bounded, arcwise connected sets in R 2 which for any S; T 2 S where S \ T 6 = ;, it holds that S \ T is arcwise connected. Given S 2 G which is triangle-free, we show that provided S is suu-ciently large there exists a subcollection S 0 S of at most 5 sets with the property that the sets of S surrounded by S 0 induce a...
متن کاملColouring Arcwise Connected Sets in the Plane I
Let G be the family of ®nite collections S where S is a collection of bounded, arcwise connected sets in R which for any S;T A S where S VT 0h, it holds that S VT is arcwise connected. We investigate the problem of bounding the chromatic number of the intersection graph G of a collection S A G. Assuming G is triangle-free, suppose there exists a closed Jordan curve C HR such that C intersects a...
متن کاملOrdered Compactifications with Countable Remainders
Countable compactifications of topological spaces have been studied in [1], [5], [7], and [9]. In [7], Magill showed that a locally compact, T2 topological space X has a countable T2 compactification if and only if it has n-point T2 compactifications for every integer n ≥ 1. We generalize this theorem to T2-ordered compactifications of ordered topological spaces. Before starting our generalizat...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Topology and its Applications
سال: 2007
ISSN: 0166-8641
DOI: 10.1016/j.topol.2006.12.006