Sentence examples for tv pn from inspiring English sources

If W1 is a TV PN space.

[[27], p. 105] (a) If V is a finite-dimensional PN space and T 1, T 2 are two topologies on V that make it into a TV space, then T 1 = T 2.   (b) If V is a TV PN space and M is a finite-dimensional linear manifold in V, then M is closed.  .

If V is a finite-dimensional PN space and T 1, T 2 are two topologies on V that make it into a TV space, then T 1 = T 2. If V is a TV PN space and M is a finite-dimensional linear manifold in V, then M is closed.

NZ, PN and TV provided scientific input.

WJ, JM, PN, NZ, TV, JvH, PS, NH and JH revised the manuscript.

+ = with PN, − = no PN.

A ϕ-Šerstnev PN space is a TV space if, and only if, it is strict.

Moreover, if ( V 1, ν, τ 1, τ 1 * ) and ( V 2, ν ′, τ 2, τ 2 * ) are α-Šerstnev PN spaces that are TV spaces, then the following statements hold: (c) Let dim V1 < ∞.

If dim V = n < ∞ and (V, ν, τ, τ*) is a PN space that is also a TV space and A is a subspace of V, then: (a) V is normable.

An α-Šerstnev PN space (V,ν, τ, τ*) is a TV space if, and only if, it is strict.

By the Theorem 2.1 we know that an equilateral space is a locally convex Š-probabilistic seminormed space but not a TV space (topological vector space) and also it is a PN space but not a TV space.