منابع مشابه
Ungar’s Theorems on Countable Dense Homogeneity Revisited
In this paper we introduce a slightly stronger form of countable dense homogeneity that for Polish spaces can be characterized topologically in a natural way. Along the way, we generalize theorems obtained by Bennett and Ungar on countable dense homogeneity.
متن کاملOpen Problems on Countable Dense Homogeneity
We survey recent development in research on countable dense homogeneity with special emphasis on open problems.
متن کاملOn Countable Dense and n-homogeneity
We prove that a connected, countable dense homogeneous space is n-homogeneous for every n, and strongly 2-homogeneous provided it is locally connected. We also present an example of a connected and countable dense homogeneous space which is not strongly 2-homogeneous. This answers in the negative Problem 136 of Watson in the Open Problems in Topology Book.
متن کاملCountable dense homogeneity and λ - sets
We show that all sufficiently nice λ-sets are countable dense homogeneous (CDH). From this fact we conclude that for every uncountable cardinal κ ≤ b there is a countable dense homogeneous metric space of size κ. Moreover, the existence of a meager in itself countable dense homogeneous metric space of size κ is equivalent to the existence of a λ-set of size κ. On the other hand, it is consisten...
متن کاملCountable Dense Homogeneity of Definable Spaces
We investigate which definable separable metric spaces are countable dense homogeneous (CDH). We prove that a Borel CDH space is completely metrizable and give a complete list of zero-dimensional Borel CDH spaces. We also show that for a Borel X ⊆ 2 the following are equivalent: (1) X is Gδ in 2 ω , (2) X is CDH and (3) X is homeomorphic to 2 or to ω . Assuming the Axiom of Projective Determina...
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: Fundamenta Mathematicae
سال: 1972
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm-75-1-33-34