Some theorems on topological manifolds

1971 ◽  
pp. 1-7 ◽  
Author(s):  
R. C. Kirby ◽  
L. C. Siebenmann
Keyword(s):  
Topological Manifolds

scholarly journals Embedding Topological $n$-Manifolds into Compact Nonstandard Topological $n$-Manifolds with Boundary

2021 ◽  
Author(s):  
Yu-Lin Chou
Keyword(s):  
Topological Manifold ◽  
Manifolds With Boundary ◽  
Manifold With Boundary ◽  
Topological Manifolds ◽  
One Point Compactification ◽  
Main Message

We show as a main message that there is a simple dimension-preserving way to openly and densely embed every topological manifold into a compact ``nonstandard'' topological manifold with boundary.This class of ``nonstandard'' topological manifolds with boundary contains the usual topological manifolds with boundary.In particular,the Alexandroff one-point compactification of every given topological $n$-manifold is a ``nonstandard'' topological $n$-manifold with boundary.

scholarly journals Metrisation of Moore spaces and abstract topological manifolds

1997 ◽  
Vol 56 (3) ◽  
pp. 395-401 ◽  
Author(s):  
David L. Fearnley
Keyword(s):  
Recent Work ◽  
Topological Spaces ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Moore Space ◽  
Global Coherence ◽  
Topological Manifolds ◽  
Necessary And Sufficient ◽  
Moore Spaces ◽  
Significant Class

The problem of metrising abstract topological spaces constitutes one of the major themes of topology. Since, for each new significant class of topological spaces this question arises, the problem is always current. One of the famous metrisation problems is the Normal Moore Space Conjecture. It is known from relatively recent work that one must add special conditions in order to be able to get affirmative results for this problem. In this paper we establish such special conditions. Since these conditions are characterised by local simplicity and global coherence they are referred to in this paper generically as “abstract topological manifolds.” In particular we establish a generalisation of a classical development of Bing, giving a proof which is complete in itself, not depending on the result or arguments of Bing. In addition we show that the spaces recently developed by Collins designated as “W satisfying open G(N)” are metrisable if they are locally separable and locally connected and regular. Finally, we establish a new necessary and sufficient condition for spaces to be metrisable.

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