Abstract
PROXIMATE AND APPROXIMATE SEQUENCES
Highlights
In this paper the author defines and discuses the concept of approximate sequences
In a compact metric space, there exists a cofinal sequence of finite regular coverings of the space
In a compact metric space Y embedded in a Hilbert cube, there exists a cofinal sequence of finite coverings V1 ≻ V2 ≻ ... ≻ Vn ≻
Summary
In this paper the author defines and discuses the concept of approximate sequences. First, in a separate section, he discusses proximate and approximate sequences. If (fn) and (fn′ ) are proximate sequences from X to Y , than there exists a cofinal sequence of finite coverings V1 ≻ V2 ≻ ... Two proximate sequences (fn) and (fn′ ) are homotopic if there exists a cofinal sequence of finite coverings V1 ≻ V2 ≻ ...
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