On absolutely closed multivalued mappings of topological spaces

Miodrag Mi\v si\'c

Abstract: We present results concerning absolute closeness of multivalued mappings for some well-known classes of pointwise closed mappings. The main results are the characterizations of absolute closeness for cofinally continuous and for residually continuous multivalued mappings. We found necessary and sufficient conditions so that the multivalued mapping $F:X\longrightarrow Y$ cannot be extended to a cofinally or a residually continuous mapping $F:X^*\longrightarrow Y$ from a space $X^*$ in which $X$ is a proper dense subset. We also proved some characterizations of cofinally and residually continuous mappings.

Classification (MSC2000): 54C60; 54C20

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