On the weak covering homotopy property

1972 ◽  
Vol 126 (3) ◽  
pp. 243-246
Author(s):  
Derek A. Waller
Keyword(s):  
Homotopy Property

On the Homotopy Property of Nussbaum's Fixed Point Index

1982 ◽  
Vol 34 (1) ◽  
pp. 44-62
Author(s):  
Gilles Fournier ◽  
Reine Fournier
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Fixed Point Index ◽  
Point Index ◽  
Homotopy Property ◽  
Lefschetz Fixed Point Theorem ◽  
The One ◽  
Compact Map ◽  
General Conditions

In [14] R. D. Nussbaum generalized the fixed point index to a class of maps larger than the one in [5]. Unfortunately his homotopy property conditions are more restrictive than the often more readily verifiable ones of Eells-Fournier. In this paper we shall try to find an intermediate class of maps which will contain all the known examples of maps for which the index is defined and for which the condition of Eells-Fournier will imply the homotopy property.In doing so, we shall give general conditions for which the sum of a compact map and a differentiable map will be a map having a fixed point index and for which the Lefschetz fixed point theorem is true.

scholarly journals On the homotopy property of degree for multivalued noncompact maps

1980 ◽  
Vol 21 (1) ◽  
pp. 125-130
Author(s):  
J. R. L. Webb
Keyword(s):  
Topological Degree ◽  
Contraction Mappings ◽  
Homotopy Property ◽  
Compact Perturbations ◽  
Degree Of A Mapping

Over the last few years, various extensions of the topological degree of a mapping have been made so as to include non-compact perturbations of the identity. One such extension, which employs compactness conditions, has been to the class of limit compact maps which were extensively studied by Sadovsky [7]. The class is a large one as it contains all compact mappings, contraction mappings and, more generally, condensing mappings. Sadovsky [7] gives a theory of degree for maps of the form I-f, where f is limit compact, and this was extended independently and with different methods by Petryshyn and Fitzpatrick [4] and the author [9] to allow f to be a multi-valued mapping. A refinement of the methods of [9] was given by Vanderbauwhede [8].

scholarly journals On the homotopy property of degree for multivalued noncompact maps

1980 ◽  
Vol 21 (2) ◽  
pp. 125-130 ◽  
Author(s):  
J. R. L. Webb
Keyword(s):  
Topological Degree ◽  
Contraction Mappings ◽  
Homotopy Property ◽  
Compact Perturbations ◽  
Degree Of A Mapping

Over the last few years, various extensions of the topological degree of a mapping have been made so as to include non-compact perturbations of the identity. One such extension, which employs compactness conditions, has been to the class of limit compact maps which were extensively studied by Sadovsky [7]. The class is a large one as it contains all compact mappings, contraction mappings and, more generally, condensing mappings. Sadovsky [7] gives a theory of degree for maps of the form I-f, where f is limit compact, and this was extended independently and with different methods by Petryshyn and Fitzpatrick [4] and the author [9] to allow f to be a multi-valued mapping. A refinement of the methods of [9] was given by Vanderbauwhede [8].

On the Calkin Algebra and the Covering Homotopy Property, II

1977 ◽  
Vol 29 (1) ◽  
pp. 210-215
Author(s):  
John B. Conway
Keyword(s):  
Hilbert Space ◽  
Separable Hilbert Space ◽  
Compact Operators ◽  
Linear Operators ◽  
Bounded Linear Operators ◽  
Bounded Linear ◽  
Calkin Algebra ◽  
Homotopy Property ◽  
The Ideal

For a separable Hilbert space is the algebra of bounded linear operators on is the ideal of compact operators, and Π is the natural map of onto the Calkin algebra .

Generalized homotopy property

1990 ◽  
Vol 31 (1) ◽  
pp. 168-170
Author(s):  
Nguen Le An'
Keyword(s):  
Homotopy Property
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