A Selection Theorem for Simplex-valued Maps (CROSBI ID 117070)
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Ivanšić, Ivan ; Rubin, Leonard R.
engleski
A Selection Theorem for Simplex-valued Maps
This short note brings the following theorem. Suppose that a function is given from a hereditarily normal paracompact Hausdorff space to a simplicial complex, i.e. a multi-valued function. Suppose that an open cover of the space is given and on each member of the cover a continuous function into the polyhedron of the simplicial complex, which is a selection of the restriction of the given multi-valued function, then there is a continuous single-valued function (or a continuous selection) from the space into the polyhedron of a given simplicial complex.
simplex-valued map; continuous selection
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