metrizable space

[mə′trīz·ə·bəl ′spās]

(mathematics)

A topological space on which can be defined a metric whose topological structure is equivalent to the original one.

References in periodicals archive ?

Every Lindelof space (in particular, every [k.sub.[omega]]-space) and every metrizable space is Dieudonne complete.

Free Subspaces of Free Locally Convex Spaces

Dales [9] within the context of "function algebras" on a compact metrizable space. In this framework, one proves that the intersections of peak sets are sets of the same type, while the peak points are dense in the Silov boundary; in effect, their set constitutes the unique minimal boundary called, Bishop boundary (ibid.).

Boundaries and peak points in topological algebras

Moreover, since Gr(H) is closed in U(H) we have that the infinite grassmannian Gr(H) is a completely metrizable space.

Topological properties of spaces of projective unitary representations

This is equipped with the compact-open topology, and it becomes a compact metrizable space (possibly infinite dimensional) with the following natural continuous C-action:

Remark on energy density of Brody curves

Let X be a metrizable space and let d be a bounded metric on X.

The fell topology on the space of time scales for dynamic equations

A well-known result of Christensen [8, Theorem 3.3] asserts that a metrizable space X is Polish if and only if X has a fundamental compact resolution.

A Characterization of the Existence of a Fundamental Bounded Resolution for the Space [C.sub.c] (X) in Terms of X

As for the rest of topologies, combination of the following items imply any closed ball [B(H).sub.[parallel]*[parallel][less than or equal to]n] forms a second countable metrizable space which leads us to conclude (B(H), [tau]) is again Lindelof.

Operator-valued measurable functions

Since every pseudocompact space is weakly pseudocompact and pseudocompact metrizable space is compact, the following result follows from Theorem 3.7.

Notes on remainders of paratopological groups

Let X be a non compact, locally compact and metrizable space such that X = [union][K.sub.n] where [([K.sub.n]).sub.n] is an exhaustive sequence of compact subsets of X.

m-infrabarrelledness and m-convexity

The following theorem for locally compact spaces and complete metrizable spaces was proved in [19].

SELECTIONS OF SET-VALUED MAPPINGS VIA APPLICATIONS

It follows that two compact metrizable spaces [[OMEGA].sub.1], [[OMEGA].sub.2] are Baire isomorphic if and only if

Isometries of Spaces of Radon Measures

Hence (T-spaces, stratifiable spaces, Moore spaces and metrizable spaces are all D-spaces.