Relations between the K-loop and the defect of an absolute plane

2005 ◽  
Vol 47 (3-4) ◽  
pp. 305-326 ◽  
Author(s):  
Helmut Karzel ◽  
Mario Marchi
Keyword(s):  
Absolute Plane

scholarly journals Introduction of measures for segments and angles in a general absolute plane

2008 ◽  
Vol 308 (2-3) ◽  
pp. 220-230 ◽  
Author(s):  
Helmut Karzel ◽  
Mario Marchi
Keyword(s):  
Absolute Plane

A Geometric Approach to the Heine-Borel Theorem

1971 ◽  
Vol 23 (5) ◽  
pp. 845-848
Author(s):  
R. B. Killgrove ◽  
Jason Frand ◽  
William Giles ◽  
Henry Bray
Keyword(s):  
Geometric Approach ◽  
Plane Geometry ◽  
Topological Properties ◽  
Absolute Plane ◽  
Topological Plane ◽  
The Absolute

In a topological plane with strong enough topological properties one can use [6] open triangular regions to define a base for the topology. Similarly, one can use these regions to define boundedness of a set. In this setting we show that in the absolute plane geometry, the holding of the Heine-Borel theorem is equivalent to every four points being contained in some such region and that this second condition is equivalent to the parallel postulate. Thus we give two new conditions equivalent to the parallel postulate.

scholarly journals Distance in the absolute plane and Cauchy functional equations

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3585-3592 ◽  
Author(s):  
Miodrag Mateljevic ◽  
Miljan Knezevic ◽  
Marek Svetlik
Keyword(s):  
Distance Function ◽  
Functional Equations ◽  
Half Line ◽  
Constructive Approach ◽  
Absolute Plane ◽  
The Absolute

Let A denotes the absolute plane and da the distance function on it. Using a constructive approach which leads to the functional equations, we study which conditions on a ?measure? of segments on a given half-line l in the absolute plane are essential to be the restriction of da on l.

On M. T. Calapso’s Characterization of the Metric of an Absolute Plane

2009 ◽  
Vol 92 (1-2) ◽  
pp. 105-116 ◽  
Author(s):  
Victor Pambuccian ◽  
Rolf Struve
Keyword(s):  
Absolute Plane
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