Paracompactness, metacompactness, and semi-open covers

Paracompactness and Product Spaces

A topological space is called paracompact (see [2 J) if (i) it is a Hausdorff space (satisfying the T2 axiom of [l]), and (ii) every open covering of it can be refined by one which is "locally finite" ( = neighbourhood-finite; that is, every point of the space has a neighbourhood meeting only a finite number of sets of the refining covering). J. Dieudonné has proved [2, Theorem 4] that every se...

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...

Randomness and lowness notions via open covers

One of the main lines of research in algorithmic randomness is that of lowness notions. Given a randomness notion R, we ask for which sequences A does relativization to A leave R unchanged (i.e., RA = R)? Such sequences are call low for R. This question extends to a pair of randomness notions R and S , where S is weaker: for which A is S A still weaker than R? In the last few years, many result...

Semi-θ-Open Sets and New Classes of Maps

Mappings and Covering Properties in L-topological Spaces

The behavior of various types of noncompact covering properties such as paracompactness, metacompactness, subparacompactness, submetacompactness, etc., are studied under various types of fuzzy mappings such as open map, closed map, perfect map, etc. Moreover the concept of para-Lindelof space is introduced in L-topological spaces and its properties and behavior under maps are obtained.