The graph-theoretic analogue of Tietze's characterization of a convex set and its generalization
1972 ◽
Vol 72
(1)
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pp. 7-9
Keyword(s):
Introduction. One of the most satisfying theorems in the theory of convex sets states that a closed connected subset of a topological linear space which is locally convex is convex. This was first established in En by Tietze and was later extended by other authors (see (3)) to a topological linear space. A generalization of Tietze's theorem which appears in (2) shows if S is a closed subset of a topological linear space such that the set Q of points of local non-convexity of S is of cardinality n < ∞ and S ~ Q is connected, then S is the union of n + 1 or fewer convex sets. (The case n = 0 is Tietze's theorem.)
2002 ◽
Vol 34
(3)
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pp. 353-358
1989 ◽
Vol 106
(2)
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pp. 277-280
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2006 ◽
Vol 2006
◽
pp. 1-7
Keyword(s):
1966 ◽
Vol 18
◽
pp. 883-886
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Keyword(s):
2017 ◽
Vol 69
(02)
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pp. 321-337
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Keyword(s):
1967 ◽
Vol 63
(2)
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pp. 311-313
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Keyword(s):
1988 ◽
Vol 11
(3)
◽
pp. 585-588
1991 ◽
Vol 109
(2)
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pp. 351-361
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