THE CHAIN RECURRENT SET ON COMPACT TVS-CONE METRIC SPACES
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Abstract
Conley introduced attracting sets and repelling sets for a flow on a topological space and showed that if f is a flow on a compact metric space, then R(f ) = (cid:84){AU ∪ A∗ U |U is a trapping region for f }. In this paper we introduce chain recurrent set, trapping region, attracting set and repelling set for a flow f on a TVS-cone metric space and prove that if f is a flow on a compact TVS-cone metric space, then R(f ) = (cid:84){AU ∪ A∗ U |U is a trapping region for f }.
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