Hereditarily strongly cwH and other separation axioms (original) (raw)
Related papers
Topology and its Applications, 1994
A separation property called i*-normal and weaker than normality is investigated. The main results include: Under V= L, a first countable 7-normal space is cT-collectionwise Hausdorff, and in a locally compact 7-normal space any discrete collection 9 of compact sets with 19 1 <w,, can be c-separated. Under PMEA, a first countable 7-normal space is collectionwise 7-normal. Any countably paracompact 7-normal space X is normal and any countably metacompact, normal i*-cwN space is cwN.
Some types of separation axioms in topological spaces
In this paper, we introduce some types of separation axioms via ω-open sets, namely ω-regular, completely ω-regular and ω-normal space and investigate their fundamental properties, relationships and characterizations. The well-known Urysohn's Lemma and Tietze Extension Theorem are generalized to ω-normal spaces. We improve some known results. Also, some other concepts are generalized and studied via ω-open sets.
ON RGW⍺LC-SEPARATION AXIOMS IN TOPOLOGICAL SPACES.
The aim of this paper is to introduce and study two new classes of spaces, namely rgw⍺lc-𝜏0, rgw⍺lc-𝜏1, rgw⍺lc-𝜏2,rgw⍺lc-regular and rgw⍺lc-normal spaces and obtained their properties by utilizing rgw⍺lc-closed sets. Also we will present some characterizations of these spaces.
Hereditary normality of γ-spaces
Topology and its Applications, 1995
One of the classical separation axioms of topology is complete normality. A topological space X is completely normal if for every pair of subsets A and B of X which are separated (i.e.Ā ∩ B = ∅ = A ∩B) there are disjoint open sets containing A and B respectively. A standard exercise is to show that this is equivalent to hereditary normality; that is, the property that all subspaces of X are normal. Hausdorff spaces satisfying this property are commonly designated as T 5 spaces.
RW-SEPARATION AXIOMS IN TOPOLOGICAL SPACES
The aim of this paper is to introduce and study two new classes of spaces, namely Rw-normal and rw-regular spaces and obtained their properties by utilizing rw-closed sets.
Normality and properties related to compactness in hyperspaces
Proceedings of the American Mathematical Society, 1970
Introduction. Let X be a regular Ti topological space and 2X the space of all closed nonempty subsets of X with the finite topology [8, Definition 1.7]. In Ivanova has shown that if X is a noncompact ordinal space, then 2X is nonnormal. In this paper we give a new proof of this fact. This result is then used to show that several properties of 2X are equivalent to the compactness of X. It is not known if the normality of 2X is equivalent to the compactness of X. There are some partial results in this direction though. The paracompactness of 2X is shown to be equivalent to the compactness of X and the normality of 22 is also shown to be equivalent to the compactness of X. In the last part of the paper some properties related to the countable compactness of 2X are investigated. Notation. Because of our assumptions on X, X= { {x} :x£X} is a closed subset of 2X homeomorphic to X. The set <5n(X) = {FEX: F has at most ra points} is also closed. Furthermore, the space 2X is Hausdorff. For notation and further basic results on hyperspaces see