Insertion of lattice-valued functions in a monotone manner is investigated. For L a ⊲-separable completely distributive lattice (i.e. L admits a countable base which is free of supercompact elements), a monotone version of the Katětov-Tong insertion theorem
for L-valued functions is established. We also provide a monotone lattice-valued version of Urysohn’s lemma. Both results yield
new characterizations of monotonically normal spaces. Moreover, extension of lattice-valued functions under additional assumptions
is shown to characterize also monotone normality.
We investigate the relations between decreasing sequences of sets and the insertion of semi-continuous functions, and give
some characterizations of countably metacompact spaces, countably paracompact spaces, monotonically countably paracompact
spaces (MCP), monotonically countably metacompact spaces (MCM), perfectly normal spaces and stratifiable spaces.
A sufficient condition for the strict insertion of a continuous function between two comparable upper and lower semicontinuous
functions on a normal space is given. Among immediate corollaries are the classical insertion theorems of Michael and Dowker.
Our insertion lemma also provides purely topological proofs of some standard results on closed subsets of normal spaces which
normally depend upon uniform convergence of series of continuous functions. We also establish a Tietze-type extension theorem
characterizing closed Gδ-sets in a normal space.
have to be performed in s 1 (or in s 2 ) in order to make s 1 and s 2 identical, where the admitted operations are deletion of a symbol, insertion of a symbol and substitution of a symbol by a symbol. Let L max ( s 1 , s 2 ) be the maximal
Authors:Renato X. Coutinho, Eliziane S. Dávila, Wendel M. dos Santos, João B. T. Rocha, Diogo O. G. Souza, Vanderlei Folmer, and Robson L. Puntel
(20–30%). This balance between the disciplines focused is very important, since Fensham ( 2008 ) reported that the knowledge of science refers to the knowledge of the natural world and its perception is essential for the student insertion in society
Authors:D. R. Amancio, M. G. V. Nunes, O. N. Oliveira Jr., and L. da F. Costa
most representative of the topics in a paper. In other words, upon examining only these sections we wished to concentrate on the contents expressing the gist of the paper and its insertion in the research area. Nevertheless, as we shall show the results