engleski

Pseudo-compactness of direct limits

Let Z, H be spaces. We introduce the direct system A induced by the set of maps between the spaces Z and H and explore conditions under which X = dirlim A will be pseudo-compact, but not necessarily complact. We also define the concept of a space Y being an absolute extensor relativ to convergent sequences for a given space Z, which is useful in our situation and is used in formulating sufficient conditions for X = dirlim A to be pseudo-compact.

Absolute extensor; CW-complex; direct limit; long line; perfect space; pseudo-compact

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