Cell-like mappings of 𝐴𝑁𝑅’𝑠

Cell-like mappings. I

“…(This is the property described in condition (d) of Theorem 1.1.) Some of the arguments of [19] are quite similar to some in [15], as are some of the results. Hyman's result that an absolutely neighborhood contractible space is an ANR divisor translates, using Theorem 1.1 and the terminology above, as follows.…”

“…The terminology introduced in [19] and [20], Property (**), has been changed so that the present paper is now in agreement with at least part of the existing literature.…”

“…The next theorem gives a complete answer to question (1) is what was called "Property (*)" in [19]. McMillan [22] Recall that an open n-cell is a manifold homeomorphic to R n .…”

“…(In fact, the results announced in [20] are proved in this paper.) We would now like to state the main result of [19]; in order to do this we need the following property (called Property (**) in [19] and [20] [19]. In our applications below, we will not need the equivalence of (a) and (b).…”

Topological regular neighborhoods

“…Shape theory says that if this definition holds for one proper embedding X ֒→ Q, it hold for all [La2,p.499].…”