Some results on linearly Lindelöf spaces
... (i) A space X is called a D-space if, for every neighborhood assignment φ on X, there exists a locally finite in X subset A of X such that the family φ(A) = {φ(x) : x ∈ A} covers X. (ii) A space X is called a D-space if, for every neighborhood assignment φ on X, there exists a closed discrete subset ...
... (i) A space X is called a D-space if, for every neighborhood assignment φ on X, there exists a locally finite in X subset A of X such that the family φ(A) = {φ(x) : x ∈ A} covers X. (ii) A space X is called a D-space if, for every neighborhood assignment φ on X, there exists a closed discrete subset ...
A connected, locally connected infinite metric space without
... We denote by π : B(ℵ1) × I → B(ℵ1) × I/ ∼ = C(ℵ1) the map which associates to a point in B(ℵ1) × I its equivalence class with respect to the relation ∼. The quotient topology is non-metrizable, hence not suitable for our purpose, and we shall equip C(ℵ1) with the following coarser topology T. We sh ...
... We denote by π : B(ℵ1) × I → B(ℵ1) × I/ ∼ = C(ℵ1) the map which associates to a point in B(ℵ1) × I its equivalence class with respect to the relation ∼. The quotient topology is non-metrizable, hence not suitable for our purpose, and we shall equip C(ℵ1) with the following coarser topology T. We sh ...
2.1 inductive reasoning and conjecture ink.notebook
... Make a conjecture about each value or geometric relationship. (State something that is true.) ...
... Make a conjecture about each value or geometric relationship. (State something that is true.) ...
On analyticity in cosmic spaces
... Theorem 1.3 is specific for cosmic spaces. Indeed, Nω1 is not Lindelöf, not to say K-analytic; nevertheless, all metrizable continuous images of Nω1 are analytic. To see that note that every metrizable continuous image of Nω1 is second countable because Nω1 satisfies c.c.c. Furthermore, every conti ...
... Theorem 1.3 is specific for cosmic spaces. Indeed, Nω1 is not Lindelöf, not to say K-analytic; nevertheless, all metrizable continuous images of Nω1 are analytic. To see that note that every metrizable continuous image of Nω1 is second countable because Nω1 satisfies c.c.c. Furthermore, every conti ...
English
... situation arises with the homology groups –introduced by H. Poincaré in 1895− since, for a diversity of topological spaces, the algebraic structure of their associated homology groups can be calculated. There are not many algorithms to compute absolute (or relative) homotopy groups of a topological ...
... situation arises with the homology groups –introduced by H. Poincaré in 1895− since, for a diversity of topological spaces, the algebraic structure of their associated homology groups can be calculated. There are not many algorithms to compute absolute (or relative) homotopy groups of a topological ...
Available online through www.ijma.info ISSN 2229 – 5046
... Proof: If A and B are rw-open sets in a space X. Then Ac and Bc are rw-closed sets in a space X. Then by theorem (Ac)∪(Bc) is also rw-closed set in X. Therefore A∩B is rw-open set in X. Remark 2.11: The Union of two rw-open sets in X is need not be rw-open in X. Example 2.12: Let X={a,b,c,d} be a to ...
... Proof: If A and B are rw-open sets in a space X. Then Ac and Bc are rw-closed sets in a space X. Then by theorem (Ac)∪(Bc) is also rw-closed set in X. Therefore A∩B is rw-open set in X. Remark 2.11: The Union of two rw-open sets in X is need not be rw-open in X. Example 2.12: Let X={a,b,c,d} be a to ...
3-manifold
In mathematics, a 3-manifold is a space that locally looks like Euclidean 3-dimensional space. Intuitively, a 3-manifold can be thought of as a possible shape of the universe. Just like a sphere looks like a plane to a small enough observer, all 3-manifolds look like our universe does to a small enough observer. This is made more precise in the definition below.