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</script>Abstract Whyburn's unifying constructions is shown to be a function from one category of bundles over locally compact base spaces to another category of bundles over the same base spaces. This functor one-point compactifiles the fiber, commutes with the pullback functor and takes trivial bundles to trivial bundles.
Whyburn construction, Extensions of spaces (compactifications, supercompactifications, completions, etc.), fibrewise 1- point compactification, Local compactness, \(\sigma\)-compactness, Fiber bundles in algebraic topology, bundles over locally compact spaces
Whyburn construction, Extensions of spaces (compactifications, supercompactifications, completions, etc.), fibrewise 1- point compactification, Local compactness, \(\sigma\)-compactness, Fiber bundles in algebraic topology, bundles over locally compact spaces
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