On \Tone\ Reflex of Topological Space

Adam Naumowicz

University of Bialystok

Mariusz Lapinski

University of Bialystok

Summary.

This article contains a definition of $T_{1}$ reflex of a topological space as a quotient space which is $T_{1}$ and fulfils the condition that every continuous map $f$ from a topological space $T$ into $S$ being $T_{1}$ space can be considered as a superposition of two continuous maps: the first from $T$ onto its $T_{1}$ reflex and the last from $T_{1}$ reflex of $T$ into $S$.

MML Identifier: T_1TOPSP

Contents (PDF format)

Bibliography

[1] Jozef Bialas and Yatsuka Nakamura. Dyadic numbers and T$_4$ topological spaces. Journal of Formalized Mathematics, 7, 1995.

[2] Czeslaw Bylinski. Functions and their basic properties. Journal of Formalized Mathematics, 1, 1989.

[3] Czeslaw Bylinski. Functions from a set to a set. Journal of Formalized Mathematics, 1, 1989.

[4] Czeslaw Bylinski. Some basic properties of sets. Journal of Formalized Mathematics, 1, 1989.

[5] Agata Darmochwal. Families of subsets, subspaces and mappings in topological spaces. Journal of Formalized Mathematics, 1, 1989.

[6] Beata Padlewska. Families of sets. Journal of Formalized Mathematics, 1, 1989.

[7] Beata Padlewska and Agata Darmochwal. Topological spaces and continuous functions. Journal of Formalized Mathematics, 1, 1989.

[8] Konrad Raczkowski and Pawel Sadowski. Equivalence relations and classes of abstraction. Journal of Formalized Mathematics, 1, 1989.

[9] Andrzej Trybulec. Tarski Grothendieck set theory. Journal of Formalized Mathematics, Axiomatics, 1989.

[10] Andrzej Trybulec. A Borsuk theorem on homotopy types. Journal of Formalized Mathematics, 3, 1991.

[11] Zinaida Trybulec. Properties of subsets. Journal of Formalized Mathematics, 1, 1989.

[12] Edmund Woronowicz. Relations and their basic properties. Journal of Formalized Mathematics, 1, 1989.