Base-base paracompactness and subsets of the Sorgenfrey line
نویسندگان
چکیده
منابع مشابه
Base subsets of polar Grassmannians
Let ∆ be a thick building of type Xn = Cn,Dn. Let also Gk be the Grassmannian of k-dimensional singular subspaces of the associated polar space Π (of rank n). We write Gk for the corresponding shadow space of type Xn,k. Every bijective transformation of Gk preserving the class of base subsets (the shadows of apartments) is a collineation of Gk, and it is induced by a collineation of Π if n 6= 4...
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Let V and V ′ be 2n-dimensional vector spaces over fields F and F ′. Let also : V × V → F and ′: V ′ × V ′ → F ′ be non-degenerate symplectic forms. Denote by and ′ the associated (2n − 1)-dimensional projective spaces. The sets of kdimensional totally isotropic subspaces of and ′ will be denoted by Gk and G ′ k , respectively. Apartments of the associated buildings intersect Gk and G ′ k by so...
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We first provide a modified version of the proof in [3] that the Sorgenfrey line is T1. Here, we prove that it is in fact T2, a stronger result. Next, we prove that all subspaces of R (that is the real line with the usual topology) are Lindelöf. We utilize this result in the proof that the Sorgenfrey line is Lindelöf, which is based on the proof found in [8]. Next, we construct the Sorgenfrey p...
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We study three problems which involve the nature of subspaces of the Sorgenfrey Line S. It is shown that no integer power of an uncountable subspace of S can be embedded in a smaller power of S. We review the known results about the existence of uncountable X ⊆ S where X is Lindelöf. These results about Lindelöf powers are quite set-theoretic. A descriptive characterization is given of those su...
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We continue Mizar formalization of General Topology according to the book [19] by Engelking. In the article the formalization of Section 1.2 is almost completed. Namely, we formalize theorems on introduction of topologies by bases, neighborhood systems, closed sets, closure operator, and interior operator. The Sorgenfrey line is defined by a basis. It is proved that the weight of it is continuu...
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 2012
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.2012.142995