Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: The compact-open topology

Sortuj według:

Ogranicz wyniki do:

A Hilbert cube compactification of the function space with the compact-open topology

100%

Kogasaka A., Sakai K.

Open Mathematics

2009

tom 7

nr 4

670-682

Let X be an infinite, locally connected, locally compact separable metrizable space. The space C(X) of real-valued continuous functions defined on X with the compact-open topology is a separable Fréchet space, so it is homeomorphic to the psuedo-interior s = (−1, 1)ℕ of the Hilbert cube Q = [−1, 1]ℕ. In this paper, generalizing the Sakai-Uehara’s result to the non-compact case, we construct a natural compactification $$ \bar C $$(X) of C(X) such that the pair ($$ \bar C $$(X), C(X)) is homeomorphic to (Q, s). In case X has no isolated points, this compactification $$ \bar C $$(X) coincides with the space USCCF(X,) of all upper semi-continuous set-valued functions φ: X → = [−∞, ∞] such that each φ(x) is a closed interval, where the topology for USCCF(X, ) is inherited from the Fell hyperspace Cld*F(X × ) of all closed sets in X × .

Ograniczanie wyników

1 Open Mathematics

1 Kogasaka A.

1 Sakai K.

1 2009

Wyniki wyszukiwania

A Hilbert cube compactification of the function space with the compact-open topology