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On Collectionwise Hausdorff Bitopological Spaces ABSTRACT 1
... Definition 4.5 A bitopological space -, , . is said to be & Q-space if any countable intersection of arbitrary collection of -open sets is -open set. is said to be Q-space if it is & Q-space for each 1,2. Equivalently, -, , . is Q-space if any countable intersection of arb ...
... Definition 4.5 A bitopological space -, , . is said to be & Q-space if any countable intersection of arbitrary collection of -open sets is -open set. is said to be Q-space if it is & Q-space for each 1,2. Equivalently, -, , . is Q-space if any countable intersection of arb ...
ARITHMETIC OF CURVES OVER TWO DIMENSIONAL LOCAL
... filtration of degenerating abelian varieties on local fields. In this work, we use this approach to investigate the group π1c.s (X) . As mentioned by Yoshida in [12, section 2] Grothendieck’s theory of monodromy-weight filtration on Tate module of abelian varieties are valid where the residue field ...
... filtration of degenerating abelian varieties on local fields. In this work, we use this approach to investigate the group π1c.s (X) . As mentioned by Yoshida in [12, section 2] Grothendieck’s theory of monodromy-weight filtration on Tate module of abelian varieties are valid where the residue field ...
THE NON-HAUSDORFF NUMBER OF A TOPOLOGICAL SPACE 1
... Now we are ready to introduce the concept of a non-Hausdorff number of a topological space X. Definition 2.4. Let X be a topological space. We define the non-Hausdorff number nh(X) of X as follows: nh(X) := 1 + sup{|A| : A is a (maximal) finitely non-Hausdorff subset of X}. Remark 2.5. It follows fr ...
... Now we are ready to introduce the concept of a non-Hausdorff number of a topological space X. Definition 2.4. Let X be a topological space. We define the non-Hausdorff number nh(X) of X as follows: nh(X) := 1 + sup{|A| : A is a (maximal) finitely non-Hausdorff subset of X}. Remark 2.5. It follows fr ...
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... 1)2 + 1 − f (T xn )2 −→ 0. Hence, T xn −→ x0 . The continuity of T at a is thus verified. Finally, we show that T (S2 \ U ) ⊆ U . If x0 ∈ S2 \ U then T x0 = a ∈ U . If x 6= x0 and x ∈ S2 \ U then x does not belong to the closure of Br2 ,δ (a) ∩ S2 . This implies P (x) does not belongs to the closure ...
... 1)2 + 1 − f (T xn )2 −→ 0. Hence, T xn −→ x0 . The continuity of T at a is thus verified. Finally, we show that T (S2 \ U ) ⊆ U . If x0 ∈ S2 \ U then T x0 = a ∈ U . If x 6= x0 and x ∈ S2 \ U then x does not belong to the closure of Br2 ,δ (a) ∩ S2 . This implies P (x) does not belongs to the closure ...
Covering space
In mathematics, more specifically algebraic topology, a covering map (also covering projection) is a continuous function p from a topological space, C, to a topological space, X, such that each point in X has an open neighbourhood evenly covered by p (as shown in the image); the precise definition is given below. In this case, C is called a covering space and X the base space of the covering projection. The definition implies that every covering map is a local homeomorphism.Covering spaces play an important role in homotopy theory, harmonic analysis, Riemannian geometry and differential topology. In Riemannian geometry for example, ramification is a generalization of the notion of covering maps. Covering spaces are also deeply intertwined with the study of homotopy groups and, in particular, the fundamental group. An important application comes from the result that, if X is a ""sufficiently good"" topological space, there is a bijection between the collection of all isomorphism classes of connected coverings of X and the conjugacy classes of subgroups of the fundamental group of X.