Decomposition of continuity via θ-local function in ideal topological
... Theorem 3.7. Let A and B be subsets of an ideal topological space (X,τ ,I). If A and B are ∗θ-pre-t-I-sets, then A ∩ B is a ∗θ -pre-t-I-set. Remark 3.8. The union of two ∗θ-pre-t-I- sets need not be a ∗θ-pre-t-I-set as given in the following example. Example 3.8. Let (X,τ ,I) be an ideal topological ...
... Theorem 3.7. Let A and B be subsets of an ideal topological space (X,τ ,I). If A and B are ∗θ-pre-t-I-sets, then A ∩ B is a ∗θ -pre-t-I-set. Remark 3.8. The union of two ∗θ-pre-t-I- sets need not be a ∗θ-pre-t-I-set as given in the following example. Example 3.8. Let (X,τ ,I) be an ideal topological ...
On feebly compact shift-continuous topologies on the semilattice
... Proposition 1(iii) of [11] implies that for any element x ∈ expn λ the set ↑x is open-and-closed in a T1 -semitopological semilattice (expn λ, τ ) and hence by Theorem 14 from [3] we have that for any x ∈ expn λ the space ↑x is feeble compact in a feeble compact T1 -semitopological semilattice (expn ...
... Proposition 1(iii) of [11] implies that for any element x ∈ expn λ the set ↑x is open-and-closed in a T1 -semitopological semilattice (expn λ, τ ) and hence by Theorem 14 from [3] we have that for any x ∈ expn λ the space ↑x is feeble compact in a feeble compact T1 -semitopological semilattice (expn ...
Locally compact, w_1-compact spaces
... The individual sections are only loosely connected with each other, and each can be read with minimal reliance on any of the others. All through this paper, “space” means “Hausdorff topological space.” All of the spaces described are locally compact, hence Tychonoff; and all are also normal, except ...
... The individual sections are only loosely connected with each other, and each can be read with minimal reliance on any of the others. All through this paper, “space” means “Hausdorff topological space.” All of the spaces described are locally compact, hence Tychonoff; and all are also normal, except ...
A Prelude to Obstruction Theory - WVU Math Department
... Φ 2 : e2 → S 2 that contracts the boundary of e2 to e0 via a straight-line homotopy. Example. The torus in Figure 1.3 grants Φ 2 : e2 → T 2 defined by the identification of edges and, subsequently, Φ11 and Φ12 : e1i → S 1 for i = 1, 2, by identifying endpoints of each edge. Both of the these example ...
... Φ 2 : e2 → S 2 that contracts the boundary of e2 to e0 via a straight-line homotopy. Example. The torus in Figure 1.3 grants Φ 2 : e2 → T 2 defined by the identification of edges and, subsequently, Φ11 and Φ12 : e1i → S 1 for i = 1, 2, by identifying endpoints of each edge. Both of the these example ...
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.