called the expansivity constant, such that for any pair of points in there is an integer such that
Note that in this definition, can be positive or negative, and so may be expansive in the forward or backward directions.
The space is often assumed to be compact, since under that assumption expansivity is a topological property; i.e. if is any other metric generating the same topology as , and if is expansive in , then is expansive in (possibly with a different expansivity constant).
is a continuous map, we say that is positively expansive (or forward expansive) if there is a
such that, for any in , there is an such that .
where is the expansivity constant of (proof).
Concrete column shape modification with FRP shells and expansive cement concrete.(fiber reinforced polymer)(Report)
Jan 01, 2011; ABSTRACT Fiber Reinforced Polymer (FRP) composites are an effective material for strengthening circular concrete columns....