TY - JOUR
T1 - Browder’s theorem with general parameter space
AU - Solan, Eilon
AU - Solan, Omri N.
N1 - Publisher Copyright:
© 2021, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2022/2
Y1 - 2022/2
N2 - It follows from Browder (Summa Bras Math 4:183–191, 1960) that for every continuous function F: (X× Y) → Y, where X is the unit interval and Y is a nonempty, convex, and compact subset of a locally convex linear vector space, the set of fixed points of F, defined by CF: = { (x, y) ∈ X× Y: F(x, y) = y} , has a connected component whose projection to the first coordinate is X. We extend Browder’s result to the case that X is a connected and compact Hausdorff space.
AB - It follows from Browder (Summa Bras Math 4:183–191, 1960) that for every continuous function F: (X× Y) → Y, where X is the unit interval and Y is a nonempty, convex, and compact subset of a locally convex linear vector space, the set of fixed points of F, defined by CF: = { (x, y) ∈ X× Y: F(x, y) = y} , has a connected component whose projection to the first coordinate is X. We extend Browder’s result to the case that X is a connected and compact Hausdorff space.
KW - Browder’s theorem
KW - connected component
KW - fixed points
KW - index theory
UR - http://www.scopus.com/inward/record.url?scp=85121724227&partnerID=8YFLogxK
U2 - 10.1007/s11784-021-00926-5
DO - 10.1007/s11784-021-00926-5
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AN - SCOPUS:85121724227
VL - 24
JO - Journal of Fixed Point Theory and Applications
JF - Journal of Fixed Point Theory and Applications
SN - 1661-7738
IS - 1
M1 - 10
ER -