Generalized homotopy property (Q2640192)

The author introduces the following notion of generalized homotopy: Let f,g: \(X\to Y\) be continuous mappings. Suppose that there are a connected compactum T with fixed points t,s\(\in T\) and a continuous mapping F: \(X\times T\to Y\) such that \(F_ s=f\), \(F_ t=g\), where \(F_ s\) and \(F_ t\) are the restrictions of the mapping F on \(X\times \{s\}\) and \(X\times \{t\}\) respectively. In this case the mappings f and g are called T-homotopic. In particular the natural embeddings \(i_ s\) and \(i_ t\) of X into \(X\times T\) are T-homotopic. For A any H-space, homomorphisms \(i^*_ t, i^*_ s: [X\times T,A]\to [X,A]\) arise. The author investigates the question, when the equality \(i^*_ t=i^*_ s\) holds.