Homeomorphism, in mathematics, a correspondence between two figures or surfaces or other geometrical objects, defined by a one-to-one mapping that is continuous in both directions.
Where the scores are continuous in both dictionaries, we compute the RMA linear fit.
It then follows from the scaling property that (hat beta _{k}(lambda, r)) is continuous in both λ and r.
If h is continuous in ( X, g ), then H is continuous in both ( X 2, D g ) and ( X 2, Δ g ).
(c) If h is continuous in ( X, g ), then H is continuous in both ( X 2, D g ) and ( X 2, Δ g ).
Then, since (q ( x,y )) is continuous in both arguments, it is clear that q bigl( x,{mathcal{V}}(x) bigr)in C_{mathrm{loc}}( mathbb{R}).
Assume that the conditions (iii)–(v) of Theorem 3.2 and the following conditions are satisfied: is continuous in both variables and is continuous in the first variable; is u.s.c. and compact-valued.
Assume that the bifunction (F:mathcal{H}timesmathcal{H}rightarrow Bbb{R}) is continuous in the first argument and the bifunction (G mathcal{H}timesmathcal{H}rightarrowBbb{R}) is continuous in both arguments.
It is easy to prove the existence part, since the strategy space is convex, compact, and nonempty for each ; the payoff function is continuous in both and ; is concave in for any [6].
Since is convex, closed, and bounded for each ; is continuous in both and ; and is concave in for any set, at least one Nash equilibrium point exists for [12, 22].
