Quasi-metrizability
β Scribed by H.H. Hung
- Publisher
- Elsevier Science
- Year
- 1998
- Tongue
- English
- Weight
- 357 KB
- Volume
- 83
- Category
- Article
- ISSN
- 0166-8641
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π SIMILAR VOLUMES
## Abstract Every secondβcountable regular topological space __X__ is metrizable. For a given βcomputableβ topological space satisfying an axiom of computable regularity M. SchrΓΆder [10] has constructed a computable metric. In this article we study whether this metric space (__X, d__) can be consid
Since X t (x, P,, U,(x)) c U,(x), V'(x, n, m ) c U and that completes the proof.
Suppose f:X -+ f(X) = Y is a continuous furaction from one compieteiy regular Hausdorff spar t onto another. There is associated with each possible compactification g of the domain space X a compactification of the mapping f in a unique way; the mapping compactification is called the compactifkation
A graph can be metrized by assigning a length to each of its edges. Such a graph is said to be geodetic if for each pair of vertices there is a unique geodesic joining them. It is said to be normally geodetic if each of these unique geodesics is one of the geodesics in the usual metrization of the g