Open AccessTopologies and smooth maps on initial and final objects in the category of Frölicher spaces
Author(s) -
Tshidibi Augustin Batubenge,
H. Tshilombo
Publication year - 2009
Publication title -
demonstratio mathematica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.541
H-Index - 28
eISSN - 2391-4661
pISSN - 0420-1213
DOI - 10.1515/dema-2013-0183
Subject(s) - subbase , mathematics , subspace topology , network topology , base (topology) , general topology , topology (electrical circuits) , comparison of topologies , quotient space (topology) , quotient , space (punctuation) , trace (psycholinguistics) , set (abstract data type) , topological space , pure mathematics , extension topology , combinatorics , mathematical analysis , computer science , linguistics , philosophy , programming language , operating system
In this paper, we show that when the Frölicher smooth structure is induced on a subset or a quotient set, there are three natural topologies underlying the resulting object. We study these topologies and compare them in each case. It is known that the topology generated by strucure functions is the weakest one in which all functions and curves on the space are continuous. We show that on a subspace, it is rather the trace topology which has this property, while the three topologies are coincident on the quotient space. We construct a base for the Frölicher topology and using either a base or a subbase in the sense of A. Frölicher [