What is topology? Jon Woolf February, 2010
Set of tube stations Canning Town Latimer Road Stratford Farringdon P West Ruislip Cannon Street Leicester Square Sudbury Hill Finchley Central Paddington Westbourne Park Canons Park Leyton Sudbury Town Finchley Road Park Royal Westferry A H R Chalfont & Latimer Leytonstone Surrey Quays Finsbury Park Parsons Green Westminster Acton Town Hainault Ravenscourt Park Chalk Farm Limehouse Swiss Cottage Fulham Broadway Perivale White City Aldgate Hammersmith Rayners Lane Chancery Lane Liverpool Street T G Piccadilly Circus Whitechapel Aldgate East Hampstead Redbridge Charing Cross London Bridge Temple Gants Hill Pimlico Willesden Green Alperton Hanger Lane Regents Park Chesham Loughton Theydon Bois Gloucester Road Pinner Willesden Junction Amersham Harlesden Richmond M Chigwell Tooting Bec Golders Green Plaistow Wimbledon Angel Harrow-on-the-Hill Rickmansworth Chiswick Park Maida Vale Tooting Broadway Goldhawk Road Poplar Wimbledon Park Archway Hatton Cross Roding Valley Chorleywood Manor House Tottenham Court Rd Goodge Street Preston Road Wood Green Arnos Grove Heathrow Rotherhithe Clapham Common Mansion House Tottenham Hale Grange Hill Prince Regent Woodford Arsenal Hendon Central Royal Albert Clapham North Marble Arch Totteridge & Whetstone Great Portland St Pudding Mill Lane Woodside Park B High Barnet Royal Oak Clapham South Marylebone Tower Gateway Green Park Putney Bridge Baker Street High Street Kensington Royal Victoria Cockfosters Mile End Tower Hill Greenford Q Balham Highbury & Islington Ruislip Colindale Mill Hill East Tufnell Park Gunnersbury Queens Park Bank Highgate Ruislip Gardens Colliers Wood Monument Turnham Green Queensbury Barbican Hillingdon Ruislip Manor Covent Garden Moor Park Turnpike Lane Queensway Barking Holborn Russell Square Croxley Moorgate U S Barkingside Holland Park D Morden Upminster Bridge Barons Court Holloway Road Seven Sisters Dagenham East Mornington Crescent Upney Bayswater Hornchurch Shadwell Dagenham Hthway Mudchute Upton Park Becontree Hounslow Central Shepherds Bush Debden N Uxbridge Belsize Park Hounslow East Shoreditch Devons Row Neasden V Bermondsey Hounslow West Snaresbrook Dollis Hill New Cross Vauxhall Bethnal Green Hyde Park Corner South Ealing E New Cross Gate Victoria I Blackfriars South Harrow Ealing Broadway Newbury Park W Blackhorse Road Ickenham South Kensington Ealing Common North Acton Walthamstow Central Bond Street K South Kenton Earls Court North Ealing Wanstead Borough Kennington South Quay East Acton North Greenwich Wapping Boston Manor Kensal Green South Ruislip East Finchley North Harrow Warren Street Bounds Green Kensington (Olympia) South Wimbledon East India North Wembley Warwick Avenue Bow Church Kentish Town South Woodford East Putney Northfields Waterloo Bow Road Kenton Southfields Eastcote Northolt Watford Brent Cross Kew Gardens Southgate Edgware Northwick Park Wembley Central Brixton Kilburn Southwark Edgware Road Northwood Wembley Park Bromley-by-Bow Kilburn Park St. James’s Park Elephant & Castle Northwood Hills West Acton Buckhurst Hill Kings Cross St. Pancras St. Johns Wood Elm Park Notting Hill Gate West Brompton Burnt Oak Kingsbury St. Pauls Embankment O West Finchley C Knightsbridge Stamford Brook Epping Oakwood West Ham Caledonian Road L Stanmore Euston Old Street West Hampstead Camden Town Ladbroke Grove Stepney Green Euston Square Osterley West Harrow Canada Water Lambeth North Stockwell F Oval West India Quay Canary Wharf Lancaster Gate Stonebridge Park Fairlop Oxford Circus West Kensington Canning Town Latimer Road Stratford Farringdon P West Ruislip
Geometric map of the tube
Topological map of the tube
Spaces from sets with relations a b c
Spaces from sets with relations a b c
Spaces from sets with relations a b c
Spaces from sets with relations a b c
Spaces from sets with relations a b c
Spaces from sets with relations a b c
Spaces from sets with relations a a b b � = c c
Spaces as sets with relations, with relations, . . . This construction of spaces from sets with relations is very general.
Spaces as sets with relations, with relations, . . . This construction of spaces from sets with relations is very general. In a sense, all spaces arise in this way.
Spaces as sets with relations, with relations, . . . This construction of spaces from sets with relations is very general. In a sense, all spaces arise in this way. The points of a space form a set,
Spaces as sets with relations, with relations, . . . This construction of spaces from sets with relations is very general. In a sense, all spaces arise in this way. The points of a space form a set, paths in the space are relations between the start and end points.
Spaces as sets with relations, with relations, . . . This construction of spaces from sets with relations is very general. In a sense, all spaces arise in this way. The points of a space form a set, paths in the space are relations between the start and end points. A deformation of one path into another is a relation between relations.
Spaces as sets with relations, with relations, . . . This construction of spaces from sets with relations is very general. In a sense, all spaces arise in this way. The points of a space form a set, paths in the space are relations between the start and end points. A deformation of one path into another is a relation between relations. And so on through higher and higher relations.
Spaces as sets with relations, with relations, . . . This construction of spaces from sets with relations is very general. In a sense, all spaces arise in this way. The points of a space form a set, paths in the space are relations between the start and end points. A deformation of one path into another is a relation between relations. And so on through higher and higher relations. In this way we build a set with relations, and relations between relations and so on ad infinitum out of a space.
Spaces as sets with relations, with relations, . . . This construction of spaces from sets with relations is very general. In a sense, all spaces arise in this way. The points of a space form a set, paths in the space are relations between the start and end points. A deformation of one path into another is a relation between relations. And so on through higher and higher relations. In this way we build a set with relations, and relations between relations and so on ad infinitum out of a space. We can turn this set with relations etc back into a space using the previous construction.
Spaces as sets with relations, with relations, . . . This construction of spaces from sets with relations is very general. In a sense, all spaces arise in this way. The points of a space form a set, paths in the space are relations between the start and end points. A deformation of one path into another is a relation between relations. And so on through higher and higher relations. In this way we build a set with relations, and relations between relations and so on ad infinitum out of a space. We can turn this set with relations etc back into a space using the previous construction. The resulting space is ‘equivalent’ to the original one.
Homotopy theory
Homotopy theory
Homotopy theory
Homotopy theory
Homotopy theory
Homotopy theory
Homotopy theory
Homotopy theory
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