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‘His invariant had been missed completely by topologists, in spite of intense activity in closely related areas during the preceding 60 years, and it was a complete surprise.’
‘If the book has a thesis, it is that a functional analyst is an analyst, first and foremost, and not a degenerate species of a topologist.’
‘Of special interest to topologists are manifolds, which means ‘having multiple features or forms’.’
‘The Poincaré Conjecture remained unsolved during the entire twentieth century and defeated the efforts of many of the best topologists and geometers of the time.’
‘When he produced his first few results on 4-manifolds, the ideas were so new and foreign to geometers and topologists that they merely gazed in bewildered admiration.’
‘A simple way to describe topology is as a ‘rubber sheet geometry’ - topologists study those properties of shapes that remain the same when the shapes are stretched or compressed.’
‘In fact, essentially every invariant studied by topologists can be made into a representable or corepresentable functor.’
‘When topologists started to explore the world of geometric forms in higher dimensions, they found that neither the intuition nor the vocabulary of ordinary geometry was sufficient to describe and classify the new forms they discovered.’
‘Now, when modern topologists study knots, they assume the knots are constructed out of perfectly flexible, perfectly stretchable, infinitely thin string.’
‘Topology is a branch of math that is sometimes called ‘rubber-sheet geometry’ because topologists study objects that retain their spatial properties even when they are twisted into odd shapes.’
‘It was an exciting time for the topologists in Moscow for he lectured on the topology of continua and often his latest results were presented in the course shortly after he had proved them.’
‘He left topologists a treasure-trove of theorems and techniques and left the University of Texas Mathematics Department with a goal and thirteen years of good progress toward it.’
‘For now we note that his General Topology became a bible for aspiring topologists and analysts from the time it first appeared in 1955.’
‘Certainly his work in topology would make him one of the leading topologists of all time but he may be known principally for other work.’
‘To a topologist, the fact that the fish species Scarus sp. can be continuously transformed into the species Pomacanthus is entirely unremarkable.’
‘June 13, 2003 the bewildered topologist couldn't understand why it wasn't called ‘Lord of the doughnuts’.’
‘In this spirit, topologists regard any two objects that can be deformed into each other without tearing to be one and the same thing - have a look at Plus article In space, do all roads lead home?’
‘It was enough to make a topologist weep with joy.’
‘For a long time, the Alexander polynomial was one of the few tools topologists had for telling knots apart.’
‘Your comments about the cube and venus de milo are excellent - a born topologist!’