Maximal connected sets—application to microcell CDMA

1994 ◽  
Vol 7 (1) ◽  
pp. 29-32 ◽  
Author(s):  
A. Z. Tirkel ◽  
C. F. Osborne ◽  
N. Mee ◽  
G. A. Rankin ◽  
A. McAndrew
Keyword(s):  
Connected Sets

scholarly journals \mu - k - Connectedness in GTS

2014 ◽  
Vol 33 (2) ◽  
pp. 161-165
Author(s):  
Shyamapada Modak ◽  
Takashi Noiri
Keyword(s):  
Connected Sets ◽  
Separated Sets

Csaszar [4] introduced \mu - semi - open sets, \mu - preopen sets, \mu - \alpha - open sets and \mu - \beta - open sets in a GTS (X, \tau). By using the \mu - \sigma - closure, \mu - \pi - closure, \mu - \alpha - closure and \mu - \beta - closure in (X, \tau), we introduce and investigate the notions \mu - k - separated sets and \mu - k - connected sets in (X, \tau).

On The Kakeya Constant

1965 ◽  
Vol 17 ◽  
pp. 946-956 ◽  
Author(s):  
F. Cunningham ◽  
I. J. Schoenberg
Keyword(s):  
Lower Bound ◽  
Small Area ◽  
Original Position ◽  
Connected Sets ◽  
Unit Segment ◽  
Simply Connected

We shall say that a plane set D has the Kakeya property if a unit segment can be turned continuously in D through 360° back to its original position. The famous solution of this problem by A. S. Besicovitch (1; 2; 4; 5; 6), to the effect that there are sets of arbitrarily small area having the Kayeka property, leaves open the problem obtained by adding the new condition that the set D be also simply connected. Since we do not know whether there is an attainable minimum, we define the Kakeya constant K to be the greatest lower bound of areas of simply connected sets having the Kakeya property. We shall refer to such sets as Kakeya sets.

Local Connectedness of the stone-Čech Compactification

1988 ◽  
Vol 31 (2) ◽  
pp. 236-240 ◽  
Author(s):  
D. Baboolal
Keyword(s):  
Uniform Space ◽  
Finite Union ◽  
Local Connectedness ◽  
Connected Sets ◽  
Connected Spaces

AbstractA uniform space X is said to be uniformly locally connected if given any entourage U there exists an entourage V ⊂ U such that V[x] is connected for each x ∈ X. It is said to have property S if given any entourage U, X can be written as a finite union of connected sets each of which is U-small.Based on these two uniform connection properties, another proof is given of the following well known result in the theory of locally connected spaces: The Stone-Čech compactification βX is locally connected if and only if X is locally connected and pseudocompact.

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