scholarly journals A Note on Hausdorff Separation

1961 ◽  
Vol 68 (2) ◽  
pp. 164 ◽  
Author(s):  
Edwin Halfar
Keyword(s):  

2001 ◽  
Vol 26 (4) ◽  
pp. 233-237
Author(s):  
Martin M. Kovár

A considerable problem of some bitopological covering properties is the bitopological unstability with respect to the presence of the pairwise Hausdorff separation axiom. For instance, if the space is RR-pairwise paracompact, its two topologies will collapse and revert to the unitopological case. We introduce a new bitopological separation axiomτS2σwhich is appropriate for the study of the bitopological collapse. We also show that the property that may cause the collapse is much weaker than some modifications of pairwise paracompactness and we generalize several results of T. G. Raghavan and I. L. Reilly (1977) regarding the comparison of topologies.



1993 ◽  
Vol 1 (3) ◽  
pp. 285-295 ◽  
Author(s):  
M. Manuel Clementino
Keyword(s):  




2008 ◽  
Vol 159 (19) ◽  
pp. 2606-2610 ◽  
Author(s):  
Ulrich Höhle ◽  
Tomasz Kubiak
Keyword(s):  


1978 ◽  
Vol 12 (2) ◽  
pp. 247-253
Author(s):  
V D Golovin


2000 ◽  
Vol 24 (2) ◽  
pp. 139-143 ◽  
Author(s):  
Martin M. Kovár

The bitopological unstability ofRR-pairwise paracompactness in presence of pairwise Hausdorff separation axiom is caused by a bitopological property which is much weaker and more local thanRR-pairwise paracompactness. We slightly generalize some Michael's constructions and characterizeRR-pairwise paracompactness in terms of bitopologicalθ-regularity, and some other weaker modifications of pairwise paracompactness.



1987 ◽  
Vol 10 (4) ◽  
pp. 745-756
Author(s):  
Sudhir K. Goel

We define an order structure on a nonseparatedn-manifold. Here, a nonseparated manifold denotes any topological space that is locally Euclidean and has a countable basis; the usual Hausdorff separation property is not required. Our result is that an ordered nonseparatedn-manifoldXcan be realized as an ordered orbit space of a completely unstable continuous flowϕon a Hausdorff(n+1)-manifoldE.







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