Convex set in accordance with the coordinate planes in R3


Abstract in English

Let A be a set in R3. A is called a Convex set in accordance with the coordinate planes ,if and only if ,any parallel plane to any coordinate planes was intersected with A is convex set . In this research we introduced a new style in the convexity is convexity in accordance with the coordinate planes ,and got a some of results and theorems, the most important : proving that every convex set in accordance with the coordinate planes is convex set, and we have offered many examples that illustrate the relationship between starshaped set, compact set , simply connected set , coordinate convex set and convex set in accordance with the coordinate planes .

References used

BOLTYANSKI.V.G,SOLTAN,P.S,Combinotorial Geometry of Classes of Convex Sets , ( in Russian ) . Stinica .Kishinev. .1978-279P
TABALE. A .E ., ZARIF,A–One Theorem a Starshaped Sets (in Russian ) .Ezvistia . Akad .Nauk .MSSR.1994 N14-P .16-20

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