g *-closed sets in ideal topological spaces
... Theorem 2.22. Let (X, τ , I) be an ideal topological space. If A and B are subsets of X such that A⊆B⊆cl∗ (A) and A is Ig⋆ -closed, then B is Ig⋆ -closed. Proof. Since A is Ig⋆ -closed, then by Theorem 2.3 (4), cl∗ (A)−A contains no nonempty g-closed set. Since cl∗ (B)−B⊆cl∗ (A)−A and so cl∗ (B)−B c ...
... Theorem 2.22. Let (X, τ , I) be an ideal topological space. If A and B are subsets of X such that A⊆B⊆cl∗ (A) and A is Ig⋆ -closed, then B is Ig⋆ -closed. Proof. Since A is Ig⋆ -closed, then by Theorem 2.3 (4), cl∗ (A)−A contains no nonempty g-closed set. Since cl∗ (B)−B⊆cl∗ (A)−A and so cl∗ (B)−B c ...
Bc-Open Sets in Topological Spaces
... is Bc-open set. The following example shows that the intersection of two Bc-open sets need not be Bc-open set. Example 2.6. Consider the space X , as in example 2.3, There a, c BcO X and b, c BcO X , but a, c b, c c BcO X . From the above example we notice that t ...
... is Bc-open set. The following example shows that the intersection of two Bc-open sets need not be Bc-open set. Example 2.6. Consider the space X , as in example 2.3, There a, c BcO X and b, c BcO X , but a, c b, c c BcO X . From the above example we notice that t ...
THE EXACT SEQUENCE OF A SHAPE FIBRATION Q. Haxhibeqiri
... (Theorem 4.1) and when a shape fibration induces an isomorphism of homotopy pro-groups (Theorem 5.7) obtaining also the exaet sequence of shape fibration (Theorem 5.9). ...
... (Theorem 4.1) and when a shape fibration induces an isomorphism of homotopy pro-groups (Theorem 5.7) obtaining also the exaet sequence of shape fibration (Theorem 5.9). ...
Harmonic analysis of dihedral groups
... [1.6.1] Remark: For abelian groups A, the minimal translation-stable subspaces of L2 (A) are onedimensional, consisting of scalar multiples C · χ of characters χ : A → C× . In contrast, minimal stable subspaces of L2 (G) for dihedral groups G are mostly two-dimensional. Further, the parametrizing sc ...
... [1.6.1] Remark: For abelian groups A, the minimal translation-stable subspaces of L2 (A) are onedimensional, consisting of scalar multiples C · χ of characters χ : A → C× . In contrast, minimal stable subspaces of L2 (G) for dihedral groups G are mostly two-dimensional. Further, the parametrizing sc ...
A class of angelic sequential non-Fréchet–Urysohn topological groups
... subsets of E respectively. The space Eβ∗ is usually called the strong dual of E, and we have called Ec∗ the Pontryagin dual of E. The polar of a subset U ⊂ E will be denoted by U ◦ := {f ∈ E ∗ ; |f (x)| 1, ∀x ∈ U }. Next we give the analogue setting for Abelian topological groups. From now on all ...
... subsets of E respectively. The space Eβ∗ is usually called the strong dual of E, and we have called Ec∗ the Pontryagin dual of E. The polar of a subset U ⊂ E will be denoted by U ◦ := {f ∈ E ∗ ; |f (x)| 1, ∀x ∈ U }. Next we give the analogue setting for Abelian topological groups. From now on all ...
1 Facts concerning Hamel bases - East
... space E is a complete normed vector space over a field K ⊂ R (or K ⊂ C), and to exclude the trivial case, we always assume E = {0}. Notice, that a Banach space over R can be considered as a Banach space over any subfield K⊆R, simply by restricting the scalars to K. Conversely, a Banach space E over K ...
... space E is a complete normed vector space over a field K ⊂ R (or K ⊂ C), and to exclude the trivial case, we always assume E = {0}. Notice, that a Banach space over R can be considered as a Banach space over any subfield K⊆R, simply by restricting the scalars to K. Conversely, a Banach space E over K ...
