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About Non-regular N-Spaces and Characterization of Metrizable Spaces in Terms of g-function

Author: DuXiangPin
Tutor: PengLiangXue
School: Beijing University of Technology
Course: Basic mathematics
Keywords: Spatial metrics N- Space K- Network Network Regularity g- function
CLC: O189.11
Type: Master's thesis
Year: 2005
Downloads: 9
Quote: 0
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Abstract


Generalized metric space is a metric space of promotion, research beneficial to further characterize its measurability . People from metrization theorem , weakening its conditions in various ways , to get the new space classes. These spaces classes include σ- space , N- Space , La (?) Nev- space . Compared with the base , the network , k- net with a more delicate and more variable structures. Generalized metric spaces classes aim of the study is to examine one of the internal structure of these spaces . While the general topological space research , people tend to add different separation conditions . Theorem requires separability condition weaker , the more extensive the scope of theorems . This article is committed to weaken some special spatial separability Conditions. One of the issues discussed in this paper are N- space characterization of the problem under different conditions . By weakening the regularity conditions redefines the N- space , and called nonregular N- space . In this paper we prove on nonregular N- space g- function characterization theorem , and then use this characterization theorem has been Fréchet space X nonregular of N- space necessary and sufficient conditions . The second research question is to discuss a metric space g- function characterization , this paper gives a metric space g- function characterization of a new form . The main conclusions are as follows: Theorem 1 a Fréchet space X nonregular of N- space if and only if it has a network F = ∪ n = 1 ∞ F n met : (?) n ∈ N, F n is a locally finite closed covering of X , and for (?) x ∈ X and satisfy x ∈ F n ∈ F n of F n , have {F n | n ∈ N} is a point X at a network or it is hcp the . Theorem 2 Let X be a metric space , then there exists a g- function satisfies the following conditions : (ks) for x ∈ X and X is a sequence {x n }, {y n } , if x n → x, x n ∈ g (n, y n ), then y n - → x;

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CLC: > Mathematical sciences and chemical > Mathematics > Geometry, topology > Topology ( the situation in geometry ) > General topology > Topological space ( spatial topology )
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