A sequence ${T_n}_{n=1}^{infty}$ of bounded linear  operators on a separable infinite dimensional Hilbert space $mathcal{H}$ is called subspace-diskcyclic with respect to the closed subspace $Msubseteq mathcal{H},$ if there exists a vector $xin mathcal{H}$ such that the disk-scaled orbit ${alpha T_n x: nin mathbb{N}, alpha inmathbb{C}, | alpha | leq 1}cap M$ is dense in $M$. The goal of t...

We construct various isometry groups of Urysohn space (the unique complete separable metric space which is universal and homogeneous), including abelian groups which act transitively, and free groups which are dense in the full isometry group.

We construct various isometry groups of Urysohn space (the unique complete separable metric space that is universal and homogeneous), including abelian groups which act transitively, and free groups which are dense in the full isometry group.

Let be a proper l.s.c. convex function on a real Hilbert space H. We show that if H is separable, then 4> is twice differentiate in some sense on a dense subset of the graph of d.

A space is called d-separable if it has a dense subset representable as the union of countably many discrete subsets. We answer several problems raised by V. V. Tkachuk by showing that (1) X is d-separable for every T1 space X; (2) if X is compact Hausdorff then X is d-separable; (3) there is a 0-dimensional T2 space X such that X2 is dseparable but X1 (and hence X) is not; (4) there is a 0-dim...

We show that it is consistent with ZF that there is a dense-in-itself compact metric space (X, d) which has the countable chain condition (ccc), but X is neither separable nor second countable. It is also shown that X has an open dense subspace which is not paracompact and that in ZF the Principle of Dependent Choice, DC, does not imply the disjoint union of metrizable spaces is normal .

We show that every separable $C^$-algebra of real rank zero tensorially absorbs the Jiang–Su algebra contains a dense set generators. It follows that, in classifiable, simple, nuclear $C^$-algebra, generic element is generator.

As usual, we equip an infinite-dimensional separable Hilbert space 2 by such nonzero σ -finite Borel measures which are invariant with respect to everywhere dense vector subspaces and study duality between such measures and Baire category. Section 1 contains constructions of nontrivialσ -finite Borel measures, which are defined in the infinite-dimensional separable Hilbert space 2 and are invar...

Let M be a separable compact Hausdorff space with dim M ≤ 2 and θ : M → M be a homeomorphism with prime period p (p ≥ 2). Set Mθ = {x ∈ M | θ(x) = x} 6= ∅ and M0 = M\Mθ. Suppose that M0 is dense in M and H(M0/θ,Z) ∼= 0, H(χ(M0/θ),Z) ∼= 0. Let M ′ be another separable compact Hausdorff space with dim M ′ ≤ 2 and θ′ be the self–homeomorphism of M ′ with prime period p. Suppose that M ′ 0 = M ′\M ...