On Feebly Compact Semitopological Semilattice expn λ

Feebly compact paratopological groups and real-valued functions

We present several examples of feebly compact Hausdorff paratopological groups (i.e., groups with continuous multiplication) which provide answers to a number of questions posed in the literature. It turns out that a 2-pseudocompact, feebly compact Hausdorff paratopological group G can fail to be a topological group. Our group G has the Baire property, is Fréchet–Urysohn, but it is not precompa...

Remarks on extremally disconnected semitopological groups

Answering recent question of A.V. Arhangel’skii we construct in ZFC an extremally disconnected semitopological group with continuous inverse having no open Abelian subgroups.

Semilattice Operations on Finite Subsets

In the article we deal with a binary operation that is associative, commutative. We define for such an operation a functor that depends on two more arguments: a finite set of indices and a function indexing elements of the domain of the operation and yields the result of applying the operation to all indexed elements. The definition has a restriction that requires that either the set of indices...

Feebly Secure Cryptographic Primitives *

In 1992, A. Hiltgen [9] provided first constructions of provably (slightly) secure cryptographic primitives, namely feebly one-way functions. These functions are provably harder to invert than to compute, but the complexity (viewed as the circuit complexity over circuits with arbitrary binary gates) is amplified only by a constant factor (in Hiltgen’s works, the factor approaches 2). In traditi...

Topology Proceedings 9 (1984) pp. 105-121: FEEBLY COMPACT SPACES, MARTIN'S AXIOM, AND "DIAMOND"