Monotone versions of δ-normality

Monotone versions of countable paracompactness

“…The Alexandroff duplicate of the unit interval [0, 1] is compact, therefore MCP, and monotonically normal but not stratifiable (as it is not perfect). However, it is first countable and regular, so by a result in [6], if X × [0, 1] were mδn, it would be monotonically normal and therefore X would be stratifiable.…”

“…Replacing We discuss mδn in more detail in [6], for the present we restrict our attention to the relationship between MCP and mδn. Example 6 There exists an MCP space that is not mδn, hence its product with [0, 1] is not mδn.…”

“…Then h is lower semicontinuous and strictly positive. By (6) there exists a real-valued upper semicontinuous function χ(h, 1) such that 0 < χ(h, 1) h. Let ψ(g) = 1/χ(h, 1). Then ψ(g) is lower semicontinuous and |g| < (|g| + 1) * ψ(g).…”

“…Definition 4 A space X is monotonically δ-normal (mδn) iff there is an operator H assigning to each pair of disjoint closed sets C and D, at least one of which is a regular We discuss mδn in more detail in [6], for the present we restrict our attention to the relationship between MCP and mδn.…”

Monotone insertion of semi-continuous functions on stratifiable spaces

“…C. Good and L. Haynes [5] gave a definition that a space X is said to be δ-stratifiable, if there is an operator U assigning to each regular…”