Uncountably many pairwise disjoint copies of one metrizable compactum in another

Spaces of Uncountably Many Dimensions*

Riemann in his Habilitations Schrift of 1854 suggested the notion of ^-dimensional space (where n is a natural number) as an extension of the notion of three-dimensional euclidean space. Hubert extended the notion still further by defining a space of a countably infinite number of dimensions. Fréchetf in 1908 defined two other spaces of countably many dimensions, which he called D„ and J3W. Tyc...

Vertex-disjoint Copies of K

Let G be a graph of order n. Let K− l be the graph obtained from Kl by removing one edge. In this paper, we propose the following conjecture: Let G be a graph of order n ≥ lk with δ(G) ≥ (n−k+1) l−3 l−2 +k−1. Then G has k vertex-disjoint K− l . This conjecture is motivated by Hajnal and Szemerédi’s [6] famous theorem. In this paper, we verify this conjecture for l = 4.

UNCOUNTABLY MANY DIFFERENT INVOLUTIONS OF 5s

Vertex-disjoint copies of K4- in graphs

Let K− 4 denote the graph obtained from K4 by removing one edge. Let k be an integer with k ≥ 2. Kawarabayashi conjectured that if G is a graph of order n ≥ 4k + 1 with σ2(G) ≥ n + k, then G has k vertex-disjoint copies of K− 4 . In this paper, we settle this conjecture affirmatively.

Extending Baire property by uncountably many sets

We prove that if ZFC is consistent so is ZFC + “for any sequence (An) of subsets of a Polish space 〈X, τ〉 there exists a separable metrizable topology τ ′ on X with B(X, τ) ⊆ B(X, τ ′), MGR(X, τ ′) ∩ B(X, τ) = MGR(X, τ) ∩B(X, τ) and An Borel in τ ′ for all n.” This is a category analogue of a theorem of Carlson on the possibility of extending Lebesgue measure to any countable collection of sets...