Open covers and the square bracket partition relation

Square - Partition Congruences

The combinatorics of open covers (II)

We continue to investigate various diagonalization properties for sequences of open covers of separable metrizable spaces introduced in Part I. These properties generalize classical ones of Rothberger, Menger, Hurewicz, and Gerlits-Nagy. In particular, we show that most of the properties introduced in Part I are indeed distinct. We characterize two of the new properties by showing that they are...

The Entropy of Co-Compact Open Covers

Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space (compactness and metrizability are not necessarily required). This is achieved through the consideration of co-compact covers of the space. The advantages of co-compact entropy include: (1) it does not require the space to be compact and, thus, generalizes Adler, Konhe...

The square root law of steganographic capacity for Markov covers

It is a well-established result that steganographic capacity of perfectly secure stegosystems grows linearly with the number of cover elements—secure steganography has a positive rate. In practice, however, neither the Warden nor the Steganographer has perfect knowledge of the cover source and thus it is unlikely that perfectly secure stegosystems for complex covers, such as digital media, will...

Combinatorics of open covers (VIII)∗

For each space, Ufin(Γ,Ω) is equivalent to Sfin(Ω,O) and this selection property has game-theoretic and Ramsey-theoretic characterizations (Theorem 2). For Lindelöf space X we characterize when a subspace Y is relatively Hurewicz in X in terms of selection principles (Theorem 9), and for metrizable X in terms of basis properties, and measurelike properties (Theorems 14 and 16). Using the Contin...