environ
vocabularies HIDDEN, NUMBERS, SUBSET_1, XREAL_0, ORDINAL1, PRE_TOPC, EUCLID, ARYTM_1, ARYTM_3, SUPINF_2, XBOOLE_0, FUNCOP_1, ORDINAL2, TOPS_1, RCOMP_1, XXREAL_0, METRIC_1, TARSKI, STRUCT_0, REAL_1, COMPLEX1, SETFAM_1, PCOMPS_1, TOPS_2, T_0TOPSP, CONNSP_2, FUNCT_1, RELAT_1, CARD_1, SQUARE_1, TOPMETR, MEMBERED, XXREAL_1, XXREAL_2, WAYBEL23, COMPTS_1, RLVECT_3, NATTRA_1, ZFMISC_1, FRECHET, CARD_3, MFOLD_1, FUNCT_2, NAT_1, XCMPLX_0;
notations HIDDEN, TARSKI, XBOOLE_0, SUBSET_1, SETFAM_1, FUNCT_1, TOPS_2, RELAT_1, RELSET_1, FUNCT_2, ORDINAL1, NUMBERS, XCMPLX_0, XREAL_0, XXREAL_0, COMPLEX1, STRUCT_0, PRE_TOPC, METRIC_1, TOPREAL9, TOPS_1, RLVECT_1, BORSUK_3, CONNSP_2, TSEP_1, METRIZTS, PCOMPS_1, COMPTS_1, EUCLID, SQUARE_1, TOPMETR, TMAP_1, XXREAL_1, MEMBERED, XXREAL_2, WAYBEL23, CANTOR_1, CARD_1, TDLAT_3, ZFMISC_1, CARD_3, YELLOW_8, FRECHET;
definitions TARSKI, FUNCT_1;
theorems TOPRNS_1, XREAL_0, TARSKI, FUNCT_2, EUCLID, XBOOLE_1, FUNCOP_1, JORDAN2C, XCMPLX_1, ABSVALUE, XXREAL_1, XXREAL_2, GOBOARD6, XREAL_1, RLVECT_1, ORDINAL1, ZFMISC_1, SETFAM_1, PRE_TOPC, TOPS_1, CONNSP_2, METRIZTS, PCOMPS_1, T_0TOPSP, YELLOW14, TOPGRP_1, XBOOLE_0, TSEP_1, BORSUK_3, TOPREAL9, BORSUK_4, RELAT_1, FUNCT_1, TOPALG_1, TOPS_2, JGRAPH_1, RELSET_1, SQUARE_1, EUCLID_2, XXREAL_0, JGRAPH_2, TOPMETR, TOPREAL3, JORDAN6, GOBOARD9, RCOMP_1, JORDAN, WAYBEL23, YELLOW12, MEMBERED, JGRAPH_3, JGRAPH_5, TDLAT_3, FRECHET, CARD_3, YELLOW_8, RLVECT_4;
schemes FUNCT_2, TREES_2;
registrations XBOOLE_0, XXREAL_0, XREAL_0, XCMPLX_0, NAT_1, MEMBERED, STRUCT_0, EUCLID, VALUED_0, FINSEQ_1, FUNCT_1, RELAT_1, PRE_TOPC, TOPS_1, CARD_1, TSEP_1, TOPREAL9, COMPLEX1, TMAP_1, COMPTS_1, TOPMETR, XXREAL_2, METRIZTS, TOPREAL1, YELLOW13, KURATO_2, SUBSET_1, RELSET_1, FUNCT_2, SQUARE_1;
constructors HIDDEN, TOPREAL9, TOPREALB, SQUARE_1, FUNCSDOM, TOPS_1, BORSUK_3, METRIZTS, COMPLEX1, BINOP_2, TMAP_1, WAYBEL23, CANTOR_1, TDLAT_3, YELLOW_8, FRECHET, SEQ_4, NUMBERS;
requirements HIDDEN, NUMERALS, BOOLE, SUBSET, ARITHM, REAL;
equalities XCMPLX_0, ALGSTR_0, STRUCT_0, PCOMPS_1, TOPREAL9, SQUARE_1, TMAP_1, WAYBEL23, ORDINAL1;
expansions TARSKI, FUNCT_1, WAYBEL23;
Lm1:
for n being Nat
for M being non empty TopSpace st M is n -locally_euclidean holds
for p being Point of M ex U being a_neighborhood of p ex B being non empty ball Subset of (TOP-REAL n) st U,B are_homeomorphic
set T = (TOP-REAL 0) | ([#] (TOP-REAL 0));
Lm2:
(TOP-REAL 0) | ([#] (TOP-REAL 0)) = TopStruct(# the carrier of (TOP-REAL 0), the topology of (TOP-REAL 0) #)
by TSEP_1:93;